Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #14271025 | C2 | semidirect |
| 4. #14270900 | C2 | semidirect |
| 5. #14270898 | C2 | semidirect |
| 6. #14270896 | C2 | semidirect |
| 7. C29×#328 | C2 | semidirect |
| 8. C2×#90809 | C4 | semidirect |
| 11. #11745308 | C4 | semidirect |
| 15. #11745257 | C4 | semidirect |
| 18. #11745254 | C4 | semidirect |
| 124. #328 | D29 | semidirect |
| 154. C29 | #1516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271676 | 2 |
| C22⋊C8×D29 | 2 |
| #14271025 | 2 |
| #14270900 | 2 |
| #14270898 | 2 |
| #14270896 | 2 |
| C29×#328 | 2 |
| #1516 | 29 |