Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #14271878 | C2 | semidirect |
| 2. #14271818 | C2 | semidirect |
| 3. #14271561 | C2 | semidirect |
| 4. #14271486 | C2 | semidirect |
| 5. #14271480 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 7. #14271443 | C2 | semidirect |
| 8. #14271413 | C2 | semidirect |
| 9. #14271242 | C2 | semidirect |
| 10. #14271204 | C2 | semidirect |
| 11. C4×D8×C29 | C2 | semidirect |
| 100. C8×C29 | #41 | semidirect |
| 130. C4×D8 | D29 | semidirect |
| 168. C29 | #3354 | semidirect |
| 229. C8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271878 | 2 |
| #14271818 | 2 |
| #14271561 | 2 |
| #14271486 | 2 |
| #14271480 | 2 |
| #14271453 | 2 |
| #14271443 | 2 |
| #14271413 | 2 |
| #14271242 | 2 |
| #14271204 | 2 |
| C4×D8×C29 | 2 |
| #3354 | 29 |