Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×#66946 | C2 | semidirect |
| 3. C2×C11×#107 | C2 | semidirect |
| 4. C2×C8×Dic11 | C2 | semidirect |
| 5. C2×#66873 | C2 | semidirect |
| 6. #10622485 | C2 | direct (N × H) |
| 14. C2×D88 | C4 | semidirect |
| 17. #66946 | C22 | semidirect |
| 18. C11×#107 | C22 | semidirect |
| 19. C8×Dic11 | C22 | semidirect |
| 20. #66873 | C22 | semidirect |
| 28. C2×D44 | C2×C4 | semidirect |
| 32. C2×C8×C11 | C2×C4 | semidirect |
| 41. D88 | C2×C4 | semidirect |
| 55. C2×Dic11 | D8 | semidirect |
| 60. D44 | C22×C4 | semidirect |
| 62. C8×C11 | C22×C4 | semidirect |
| 67. C2×#107 | D11 | semidirect |
| 83. Dic11 | C2×D8 | semidirect |
| 95. #107 | C2×D11 | semidirect |
| 98. C2×C11 | C4×D8 | semidirect |
| 117. C2×C8 | C4×D11 | semidirect |
| 124. C11 | C2×C4×D8 | semidirect |
| 145. C8 | C2×C4×D11 | semidirect |
| 161. C2 | #10622485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D88 | 2 |
| C2×#66946 | 2 |
| C2×C11×#107 | 2 |
| C2×C8×Dic11 | 2 |
| C2×#66873 | 2 |
| #10622485 | 2 |
| C2×C4×D8 | 11 |