Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271978 | C2 | semidirect |
| 2. #14271977 | C2 | semidirect |
| 3. #14271541 | C2 | semidirect |
| 4. #14271438 | C2 | semidirect |
| 5. #14271436 | C2 | semidirect |
| 6. #14271435 | C2 | semidirect |
| 7. #14271346 | C2 | semidirect |
| 8. #14271344 | C2 | semidirect |
| 9. #14271280 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#578 | C2 | semidirect |
| 144. #578 | D29 | semidirect |
| 191. C29 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271978 | 2 |
| #14271977 | 2 |
| #14271541 | 2 |
| #14271438 | 2 |
| #14271436 | 2 |
| #14271435 | 2 |
| #14271346 | 2 |
| #14271344 | 2 |
| #14271280 | 2 |
| #14271278 | 2 |
| C29×#578 | 2 |
| #3293 | 29 |