Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21454619 | C2 | semidirect |
| 3. C2×#16839573 | C2 | semidirect |
| 4. #21446696 | C2 | semidirect |
| 5. #21443924 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#2140 | C2 | semidirect |
| 11. #16840198 | C4 | semidirect |
| 48. #14519717 | C2×C4 | semidirect |
| 63. C2×D8×C61 | C2×C4 | semidirect |
| 115. Dic244 | C22⋊C4 | semidirect |
| 117. D488 | C22⋊C4 | semidirect |
| 182. #2140 | D61 | semidirect |
| 212. C61 | #13025 | semidirect |
| 227. C2×D8 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840198 | 2 |
| #21454619 | 2 |
| C2×#16839573 | 2 |
| #21446696 | 2 |
| #21443924 | 2 |
| #21443902 | 2 |
| C61×#2140 | 2 |
| #13025 | 61 |