Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#11745274 | C2 | semidirect |
| 3. #14271712 | C2 | semidirect |
| 4. #14271711 | C2 | semidirect |
| 5. #14271558 | C2 | semidirect |
| 6. #14271557 | C2 | semidirect |
| 7. #14271554 | C2 | semidirect |
| 8. #14271551 | C2 | semidirect |
| 9. #14271550 | C2 | semidirect |
| 10. #97×D29 | C2 | semidirect |
| 11. C29×#496 | C2 | semidirect |
| 79. C8×D29 | D4 | semidirect |
| 137. #496 | D29 | semidirect |
| 174. C29 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745278 | 2 |
| C2×#11745274 | 2 |
| #14271712 | 2 |
| #14271711 | 2 |
| #14271558 | 2 |
| #14271557 | 2 |
| #14271554 | 2 |
| #14271551 | 2 |
| #14271550 | 2 |
| #97×D29 | 2 |
| C29×#496 | 2 |
| #3150 | 29 |