Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
402 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 144 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. #14272197 | C2 | semidirect |
| 2. #14272196 | C2 | semidirect |
| 3. #14272193 | C2 | semidirect |
| 4. #14272192 | C2 | semidirect |
| 5. #14272187 | C2 | semidirect |
| 6. #14272137 | C2 | semidirect |
| 7. #14272136 | C2 | semidirect |
| 8. #14272134 | C2 | semidirect |
| 12. C2×#90800 | C22 | semidirect |
| 13. C22×#6599 | C22 | semidirect |
| 16. C2×#90796 | C22 | semidirect |
| 17. C2×D29⋊C8 | C22 | semidirect |
| 29. C22⋊#6599 | C22 | semidirect |
| 30. #11745220 | C22 | semidirect |
| 33. #11745219 | C22 | semidirect |
| 34. #11745218 | C22 | semidirect |
| 35. C4⋊#6599 | C22 | semidirect |
| 36. C4×#6599 | C22 | semidirect |
| 169. C29 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272197 | 2 |
| #14272196 | 2 |
| #14272193 | 2 |
| #14272192 | 2 |
| #14272187 | 2 |
| #14272137 | 2 |
| #14272136 | 2 |
| #14272134 | 2 |
| #14271671 | 2 |
| #2978 | 29 |