Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D116 | C2 | semidirect |
| 2. #14271509 | C2 | semidirect |
| 3. #14271443 | C2 | semidirect |
| 4. #14271355 | C2 | semidirect |
| 5. Q8×#6597 | C2 | semidirect |
| 6. C4×#90782 | C2 | semidirect |
| 7. C29×#550 | C2 | semidirect |
| 46. Q8×C29 | D8 | semidirect |
| 58. D116 | #41 | semidirect |
| 77. #550 | D29 | semidirect |
| 105. C29 | #3358 | semidirect |
| 129. Q8 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D116 | 2 |
| #14271509 | 2 |
| #14271443 | 2 |
| #14271355 | 2 |
| Q8×#6597 | 2 |
| C4×#90782 | 2 |
| C29×#550 | 2 |
| #3358 | 29 |