Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #14271472 | C2 | semidirect |
| 4. #14271468 | C2 | semidirect |
| 5. #14271456 | C2 | semidirect |
| 6. #14271446 | C2 | semidirect |
| 45. C2×Q8×C29 | Q8 | semidirect |
| 172. C29 | #3078 | semidirect |
| 177. C2×Q8 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271472 | 2 |
| #14271468 | 2 |
| #14271456 | 2 |
| #14271446 | 2 |
| #14271206 | 2 |
| #14271205 | 2 |
| #14271186 | 2 |
| #14271172 | 2 |
| C29×#419 | 2 |
| #3078 | 29 |