Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#11745294 | C2 | semidirect |
| 2. C2×#11745266 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271551 | C2 | semidirect |
| 5. #14271546 | C2 | semidirect |
| 6. #14271538 | C2 | semidirect |
| 7. #14271118 | C2 | semidirect |
| 8. C22×D8×C29 | C2 | semidirect |
| 16. #11745302 | C22 | semidirect |
| 18. #11745298 | C22 | semidirect |
| 19. C2×#90783 | C22 | semidirect |
| 21. C2×#90782 | C22 | semidirect |
| 24. C2×Dic116 | C22 | semidirect |
| 26. C2×D232 | C22 | semidirect |
| 27. C2×#90773 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 45. C2×C8×C29 | D4 | semidirect |
| 54. #90777 | D4 | semidirect |
| 99. C22×D8 | D29 | semidirect |
| 131. C29 | #3155 | semidirect |
| 154. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C2×#11745266 | 2 |
| #14271730 | 2 |
| #14271551 | 2 |
| #14271546 | 2 |
| #14271538 | 2 |
| #14271118 | 2 |
| C22×D8×C29 | 2 |
| #3155 | 29 |