Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #14272027 | C2 | semidirect |
| 4. #14272026 | C2 | semidirect |
| 5. #14272025 | C2 | semidirect |
| 6. #14272024 | C2 | semidirect |
| 40. #90772 | C8 | semidirect |
| 58. C8×C29 | C2×C8 | semidirect |
| 60. #6597 | C2×C8 | semidirect |
| 100. C29 | #1565 | semidirect |
| 138. C8 | D29⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272182 | 2 |
| D29⋊(C4⋊C8) | 2 |
| #14272027 | 2 |
| #14272026 | 2 |
| #14272025 | 2 |
| #14272024 | 2 |
| #14271115 | 2 |
| #1565 | 29 |