Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271498 | C2 | semidirect |
| 4. #14271470 | C2 | semidirect |
| 5. #14271385 | C2 | semidirect |
| 6. #14271319 | C2 | semidirect |
| 8. #14271268 | C2 | semidirect |
| 9. #14271261 | C2 | semidirect |
| 10. #14271220 | C2 | semidirect |
| 11. C2×C4×Q8×C29 | C2 | semidirect |
| 128. C2×C4×Q8 | D29 | semidirect |
| 174. C29 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271697 | 2 |
| #14271498 | 2 |
| #14271481 | 2 |
| #14271470 | 2 |
| #14271385 | 2 |
| #14271319 | 2 |
| #14271302 | 2 |
| #14271268 | 2 |
| #14271261 | 2 |
| #14271220 | 2 |
| C2×C4×Q8×C29 | 2 |
| #3117 | 29 |