Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #14271886 | C2 | semidirect |
| 2. #14271525 | C2 | semidirect |
| 3. #14271515 | C2 | semidirect |
| 4. #14271455 | C2 | semidirect |
| 5. #14271440 | C2 | semidirect |
| 7. #14271368 | C2 | semidirect |
| 8. #14271294 | C2 | semidirect |
| 9. #14271263 | C2 | semidirect |
| 11. D4×Q8×C29 | C2 | semidirect |
| 119. D4×Q8 | D29 | semidirect |
| 163. C29 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271525 | 2 |
| #14271515 | 2 |
| #14271455 | 2 |
| #14271440 | 2 |
| #14271378 | 2 |
| #14271368 | 2 |
| #14271294 | 2 |
| #14271263 | 2 |
| C4×#90782 | 2 |
| D4×Q8×C29 | 2 |
| #3367 | 29 |