Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #21446655 | C2 | semidirect |
| 3. #21445844 | C2 | semidirect |
| 4. #21444388 | C2 | semidirect |
| 5. C61×#1752 | C2 | semidirect |
| 6. C22×D488 | C4 | semidirect |
| 12. C2×#14519711 | C4 | semidirect |
| 14. C2×#14519699 | C4 | semidirect |
| 146. C8×C61 | #99 | semidirect |
| 174. #1752 | D61 | semidirect |
| 201. C61 | #9785 | semidirect |
| 324. C8 | #14519691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839998 | 2 |
| #21446655 | 2 |
| #21445844 | 2 |
| #21444388 | 2 |
| C61×#1752 | 2 |
| #9785 | 61 |