Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
696 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16840191 | C2 | semidirect |
| 2. #21457577 | C2 | semidirect |
| 3. #21447902 | C2 | semidirect |
| 4. #21447856 | C2 | semidirect |
| 5. #21447739 | C2 | semidirect |
| 6. C4×Dic488 | C2 | semidirect |
| 7. C16×D244 | C2 | semidirect |
| 8. C61×#2246 | C2 | semidirect |
| 41. Dic488 | D4 | semidirect |
| 123. C4×C61 | #508 | semidirect |
| 131. #2246 | D61 | semidirect |
| 162. C61 | #33853 | semidirect |
| 259. C4 | #16840191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840191 | 2 |
| #21457577 | 2 |
| #21447902 | 2 |
| #21447856 | 2 |
| #21447739 | 2 |
| C4×Dic488 | 2 |
| C16×D244 | 2 |
| C61×#2246 | 2 |
| #33853 | 61 |