Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14271711 | C2 | semidirect |
| 3. C4×#90809 | C2 | semidirect |
| 4. #14271383 | C2 | semidirect |
| 5. #14271377 | C2 | semidirect |
| 6. #14271373 | C2 | semidirect |
| 7. #14271369 | C2 | semidirect |
| 8. #14271355 | C2 | semidirect |
| 9. C4⋊C8×D29 | C2 | semidirect |
| 10. #14271156 | C2 | semidirect |
| 11. C29×#460 | C2 | semidirect |
| 51. #90809 | D4 | semidirect |
| 137. C4×C29 | #135 | semidirect |
| 152. #460 | D29 | semidirect |
| 194. C29 | #3035 | semidirect |
| 292. 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 |
| #14271711 | 2 |
| C4×#90809 | 2 |
| #14271383 | 2 |
| #14271377 | 2 |
| #14271373 | 2 |
| #14271369 | 2 |
| #14271355 | 2 |
| C4⋊C8×D29 | 2 |
| #14271156 | 2 |
| C29×#460 | 2 |
| #3035 | 29 |