Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1506 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 242 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×#14519865 | C2 | semidirect |
| 2. C2×#16840789 | C2 | semidirect |
| 3. #21461797 | C2 | semidirect |
| 4. #21461767 | C2 | semidirect |
| 5. #21461644 | C2 | semidirect |
| 6. #21461553 | C2 | semidirect |
| 30. C2×D61⋊C8 | D4 | semidirect |
| 95. C23×C61 | #131 | semidirect |
| 113. C2×Dic61 | #131 | semidirect |
| 172. C61 | #21442 | semidirect |
| 247. C23 | #14519865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519865 | 2 |
| C2×#16840789 | 2 |
| #21461797 | 2 |
| #21461767 | 2 |
| #21461644 | 2 |
| #21461553 | 2 |
| #21449036 | 2 |
| #21442 | 61 |