Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic29 | C2 | semidirect |
| 3. #14271496 | C2 | semidirect |
| 5. #14271468 | C2 | semidirect |
| 6. #14271387 | C2 | semidirect |
| 8. #14271270 | C2 | semidirect |
| 9. #14271266 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 11. C29×#451 | C2 | semidirect |
| 133. #451 | 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 |
|---|---|
| #14271699 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271496 | 2 |
| #14271482 | 2 |
| #14271468 | 2 |
| #14271387 | 2 |
| #14271302 | 2 |
| #14271270 | 2 |
| #14271266 | 2 |
| #14271217 | 2 |
| C29×#451 | 2 |
| #3117 | 29 |