Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271566 | C2 | semidirect |
| 3. #14271542 | C2 | semidirect |
| 4. #14271515 | C2 | semidirect |
| 5. #14271513 | C2 | semidirect |
| 7. C4×#90785 | C2 | semidirect |
| 73. C2×C4×C29 | Q16 | semidirect |
| 139. C29 | #3170 | semidirect |
| 182. C2×C4 | #90785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271566 | 2 |
| #14271542 | 2 |
| #14271515 | 2 |
| #14271513 | 2 |
| #14271402 | 2 |
| C4×#90785 | 2 |
| C2×C4×#6597 | 2 |
| C29×#533 | 2 |
| #3170 | 29 |