Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#14519722 | C2 | semidirect |
| 2. C2×#16840038 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. #21447538 | C2 | semidirect |
| 6. C2×#16839545 | C2 | semidirect |
| 7. C61×#1382 | C2 | semidirect |
| 40. C2×Dic244 | D4 | semidirect |
| 70. C2×C16×C61 | D4 | semidirect |
| 72. #108×C61 | D4 | semidirect |
| 195. #1382 | D61 | semidirect |
| 223. C61 | #13321 | semidirect |
| 263. C2×C16 | D244 | semidirect |
| 265. #108 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519722 | 2 |
| C2×#16840038 | 2 |
| #21455468 | 2 |
| C2×#16839574 | 2 |
| #21447538 | 2 |
| C2×#16839545 | 2 |
| C61×#1382 | 2 |
| #13321 | 61 |