Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #14271753 | C2 | semidirect |
| 2. #14271313 | C2 | semidirect |
| 3. #14271299 | C2 | semidirect |
| 4. #14271073 | C2 | semidirect |
| 5. #14270896 | C2 | semidirect |
| 6. #14270886 | C2 | semidirect |
| 7. C29×#328 | C2 | semidirect |
| 29. C2×Q8×C29 | D4 | semidirect |
| 42. C2×D116 | D4 | semidirect |
| 46. C4⋊C4×C29 | D4 | semidirect |
| 56. C4⋊Dic29 | D4 | semidirect |
| 132. #328 | D29 | semidirect |
| 162. C29 | #1600 | semidirect |
| 165. C2×Q8 | D116 | semidirect |
| 187. C4⋊C4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271753 | 2 |
| #14271313 | 2 |
| #14271299 | 2 |
| #14271073 | 2 |
| #14270896 | 2 |
| #14270886 | 2 |
| C29×#328 | 2 |
| #1600 | 29 |