Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271694 | C2 | semidirect |
| 2. C2×D4×Dic29 | C2 | semidirect |
| 3. #14271494 | C2 | semidirect |
| 4. #14271474 | C2 | semidirect |
| 5. #14271465 | C2 | semidirect |
| 6. #14271376 | C2 | semidirect |
| 7. #14271314 | C2 | semidirect |
| 8. #14271275 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 17. #11745298 | C22 | semidirect |
| 24. D4×Dic29 | C22 | semidirect |
| 29. #11745252 | C22 | semidirect |
| 30. #11745249 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745163 | C22 | semidirect |
| 41. #11745162 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 183. C29 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271694 | 2 |
| C2×D4×Dic29 | 2 |
| #14271494 | 2 |
| #14271474 | 2 |
| #14271465 | 2 |
| #14271376 | 2 |
| #14271314 | 2 |
| #14271275 | 2 |
| #14271260 | 2 |
| #14271217 | 2 |
| C29×#447 | 2 |
| #3114 | 29 |