Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. C22⋊C8×D29 | C2 | semidirect |
| 3. #14271010 | C2 | semidirect |
| 4. #14270901 | C2 | semidirect |
| 5. #14270899 | C2 | semidirect |
| 6. #14270897 | C2 | semidirect |
| 7. C29×#327 | C2 | semidirect |
| 8. C2×#90807 | C4 | semidirect |
| 11. #11745300 | C4 | semidirect |
| 18. #11745259 | C4 | semidirect |
| 19. #11745254 | C4 | semidirect |
| 127. #327 | D29 | semidirect |
| 155. C29 | #1501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271673 | 2 |
| C22⋊C8×D29 | 2 |
| #14271010 | 2 |
| #14270901 | 2 |
| #14270899 | 2 |
| #14270897 | 2 |
| C29×#327 | 2 |
| #1501 | 29 |