Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic58 | C2 | semidirect |
| 2. #14271496 | C2 | semidirect |
| 4. #14271467 | C2 | semidirect |
| 5. #14271382 | C2 | semidirect |
| 6. #14271318 | C2 | semidirect |
| 8. #14271268 | C2 | semidirect |
| 9. #14271263 | C2 | semidirect |
| 10. #14271220 | C2 | semidirect |
| 174. C29 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic58 | 2 |
| #14271496 | 2 |
| #14271479 | 2 |
| #14271467 | 2 |
| #14271382 | 2 |
| #14271318 | 2 |
| #14271301 | 2 |
| #14271268 | 2 |
| #14271263 | 2 |
| #14271220 | 2 |
| C29×#529 | 2 |
| #3117 | 29 |