Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 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. #14271567 | C2 | semidirect |
| 3. #14271541 | C2 | semidirect |
| 4. #14271512 | C2 | semidirect |
| 8. C4×Dic116 | C2 | semidirect |
| 9. C4×#90785 | C2 | semidirect |
| 11. C4×Q16×C29 | C2 | semidirect |
| 87. C4×D29 | Q16 | semidirect |
| 120. C4×Q16 | D29 | semidirect |
| 153. C29 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271717 | 2 |
| #14271567 | 2 |
| #14271541 | 2 |
| #14271512 | 2 |
| #14271405 | 2 |
| #14271403 | 2 |
| #14271401 | 2 |
| C4×Dic116 | 2 |
| C4×#90785 | 2 |
| C4×C8×D29 | 2 |
| C4×Q16×C29 | 2 |
| #3170 | 29 |