Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D11 | C2 | semidirect |
| 3. C22×C11×SD16 | C2 | semidirect |
| 4. C22×#4325 | C2 | semidirect |
| 5. C22×#4324 | C2 | semidirect |
| 6. C2×SD16×D11 | C2 | direct (N × H) |
| 7. C22×#4314 | C2 | semidirect |
| 8. C22×C8×D11 | C2 | semidirect |
| 10. C22×Q8×C11 | C22 | semidirect |
| 14. C2×Q8×D11 | C22 | semidirect |
| 21. C22×Dic22 | C22 | semidirect |
| 22. C2×C11×SD16 | C22 | semidirect |
| 23. C22×C8×C11 | C22 | semidirect |
| 24. C2×#4325 | C22 | semidirect |
| 25. C2×#4324 | C22 | semidirect |
| 26. C22×C11⋊C8 | C22 | semidirect |
| 27. SD16×D11 | C22 | direct (N × H) |
| 28. C2×#4314 | C22 | semidirect |
| 29. C2×C8×D11 | C22 | semidirect |
| 36. C2×Q8×C11 | C23 | semidirect |
| 45. Q8×D11 | C23 | semidirect |
| 55. C2×Dic22 | C23 | semidirect |
| 56. C11×SD16 | C23 | semidirect |
| 57. C2×C8×C11 | C23 | semidirect |
| 58. #4325 | C23 | semidirect |
| 59. #4324 | C23 | semidirect |
| 60. C2×C11⋊C8 | C23 | semidirect |
| 61. #4314 | C23 | semidirect |
| 62. C8×D11 | C23 | semidirect |
| 71. C22×D11 | SD16 | direct (N × H) |
| 74. Q8×C11 | C24 | semidirect |
| 90. Dic22 | C24 | semidirect |
| 91. C8×C11 | C24 | semidirect |
| 92. C11⋊C8 | C24 | semidirect |
| 99. C22×SD16 | D11 | direct (N × H) |
| 103. C22×C11 | C2×SD16 | semidirect |
| 108. C2×D11 | C2×SD16 | direct (N × H) |
| 120. C22×Q8 | C2×D11 | semidirect |
| 132. C2×SD16 | C2×D11 | direct (N × H) |
| 135. C22×C8 | C2×D11 | semidirect |
| 137. C2×C11 | C22×SD16 | semidirect |
| 140. D11 | C22×SD16 | direct (N × H) |
| 152. C2×Q8 | C22×D11 | semidirect |
| 170. SD16 | C22×D11 | direct (N × H) |
| 173. C2×C8 | C22×D11 | semidirect |
| 174. C11 | C23×SD16 | semidirect |
| 188. Q8 | C23×D11 | semidirect |
| 203. C8 | C23×D11 | semidirect |
| 211. C22 | SD16×D11 | direct (N × H) |
| 221. C2 | C2×SD16×D11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D11 | 2 |
| C22×D4×D11 | 2 |
| C22×C11×SD16 | 2 |
| C22×#4325 | 2 |
| C22×#4324 | 2 |
| C2×SD16×D11 | 2 |
| C22×#4314 | 2 |
| C22×C8×D11 | 2 |
| C23×SD16 | 11 |