Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#90773 | C2 | semidirect |
| 2. C22×#90783 | C2 | semidirect |
| 3. C22×#90782 | C2 | semidirect |
| 4. C2×#11745302 | C2 | semidirect |
| 5. C2×#11745298 | C2 | semidirect |
| 6. #14271551 | C2 | direct (N × H) |
| 7. C2×#11745163 | C2 | semidirect |
| 8. C22×D8×C29 | C2 | semidirect |
| 15. C2×D8×C29 | C22 | semidirect |
| 19. #11745302 | C22 | semidirect |
| 21. #11745298 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 25. C2×#90782 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 30. #11745163 | C22 | semidirect |
| 56. C2×C8×C29 | D4 | semidirect |
| 63. C2×#6597 | D4 | semidirect |
| 97. C8×C29 | C2×D4 | semidirect |
| 98. #6597 | C2×D4 | semidirect |
| 120. C22×D8 | D29 | semidirect |
| 127. C2×C29 | #496 | semidirect |
| 143. C2×D8 | C2×D29 | semidirect |
| 153. C29 | C2×#496 | semidirect |
| 184. C2×C8 | C22⋊D29 | semidirect |
| 221. C8 | C2×C22⋊D29 | semidirect |
| 242. C2 | #14271551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C22×#90783 | 2 |
| C22×#90782 | 2 |
| C2×#11745302 | 2 |
| C2×#11745298 | 2 |
| #14271551 | 2 |
| C2×#11745163 | 2 |
| C22×D8×C29 | 2 |
| C2×#496 | 29 |