Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271870 | C2 | semidirect |
| 2. #14271834 | C2 | semidirect |
| 3. #14271526 | C2 | semidirect |
| 4. #14271510 | C2 | semidirect |
| 5. #14271466 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 7. #14271358 | C2 | semidirect |
| 8. #14271356 | C2 | semidirect |
| 9. #14271293 | C2 | semidirect |
| 10. #14271272 | C2 | semidirect |
| 11. C4×D8×C29 | C2 | semidirect |
| 80. D4×C29 | #41 | semidirect |
| 134. C4×D8 | D29 | semidirect |
| 170. C29 | #3366 | semidirect |
| 218. D4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271834 | 2 |
| #14271526 | 2 |
| #14271510 | 2 |
| #14271466 | 2 |
| #14271453 | 2 |
| #14271358 | 2 |
| #14271356 | 2 |
| #14271293 | 2 |
| #14271272 | 2 |
| C4×D8×C29 | 2 |
| #3366 | 29 |