Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16839584 | C2 | semidirect |
| 2. #21447568 | C2 | semidirect |
| 3. #21447555 | C2 | semidirect |
| 4. #21447447 | C2 | semidirect |
| 5. #21445873 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 32. #14519717 | D4 | semidirect |
| 205. C61 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839584 | 2 |
| #21447568 | 2 |
| #21447555 | 2 |
| #21447447 | 2 |
| #21445873 | 2 |
| #21443926 | 2 |
| C61×#3060 | 2 |
| #13400 | 61 |