Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×D892 | C2 | semidirect |
| 2. #20297329 | C2 | direct (N × H) |
| 3. C2×#16813157 | C2 | semidirect |
| 4. C2×#16813155 | C2 | semidirect |
| 5. C2×#16813154 | C2 | semidirect |
| 6. C2×#41×C223 | C2 | semidirect |
| 11. C2×D892 | C22 | semidirect |
| 12. #16813157 | C22 | semidirect |
| 13. #16813155 | C22 | semidirect |
| 14. #16813154 | C22 | semidirect |
| 15. C2×C223⋊C8 | C22 | semidirect |
| 17. #41×C223 | C22 | semidirect |
| 18. C2×Q8×C223 | C22 | semidirect |
| 20. C2×D4×C223 | C22 | semidirect |
| 29. C223⋊C8 | C23 | semidirect |
| 33. Q8×C223 | C23 | semidirect |
| 36. D4×C223 | C23 | semidirect |
| 57. C2×C223 | AGL(1,ℤ/8) | semidirect |
| 60. C223 | C2×AGL(1,ℤ/8) | semidirect |
| 62. C2×#41 | D223 | semidirect |
| 70. #41 | C2×D223 | semidirect |
| 71. C2×Q8 | C2×D223 | semidirect |
| 77. C2×D4 | C2×D223 | semidirect |
| 90. Q8 | C22×D223 | semidirect |
| 96. D4 | C22×D223 | semidirect |
| 119. C2 | #20297329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D892 | 2 |
| #20297329 | 2 |
| C2×#16813157 | 2 |
| C2×#16813155 | 2 |
| C2×#16813154 | 2 |
| C2×#41×C223 | 2 |
| C2×AGL(1,ℤ/8) | 223 |