Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#11745278 | C2 | semidirect |
| 2. #14271714 | C2 | semidirect |
| 3. #14271711 | C2 | semidirect |
| 4. #14271544 | C2 | semidirect |
| 5. #14271542 | C2 | semidirect |
| 6. #14271539 | C2 | semidirect |
| 7. #14271536 | C2 | semidirect |
| 8. C4×C8×D29 | C2 | semidirect |
| 9. C29×#492 | C2 | semidirect |
| 59. C8×D29 | D4 | semidirect |
| 92. C4×C29 | #135 | semidirect |
| 104. #492 | D29 | semidirect |
| 133. C29 | #3147 | semidirect |
| 196. C4 | #11745278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745278 | 2 |
| #14271714 | 2 |
| #14271711 | 2 |
| #14271544 | 2 |
| #14271542 | 2 |
| #14271539 | 2 |
| #14271536 | 2 |
| C4×C8×D29 | 2 |
| C29×#492 | 2 |
| #3147 | 29 |