Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#106×D61 | C2 | semidirect |
| 3. C2×#16839572 | C2 | semidirect |
| 4. #21447429 | C2 | semidirect |
| 5. #21443926 | C2 | semidirect |
| 6. #21443925 | C2 | semidirect |
| 7. C2×C61×#360 | C2 | semidirect |
| 12. #16840000 | C4 | semidirect |
| 13. #16839995 | C4 | semidirect |
| 49. #14519711 | C2×C4 | semidirect |
| 52. #14519709 | D4 | semidirect |
| 61. C2×Q16×C61 | C2×C4 | semidirect |
| 63. C2×D8×C61 | C2×C4 | semidirect |
| 70. #106×C61 | D4 | semidirect |
| 176. C2×D61 | #360 | semidirect |
| 189. C2×#360 | D61 | semidirect |
| 218. C61 | #13001 | semidirect |
| 226. C2×Q16 | C4×D61 | semidirect |
| 228. C2×D8 | C4×D61 | semidirect |
| 260. #106 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455396 | 2 |
| C2×#106×D61 | 2 |
| C2×#16839572 | 2 |
| #21447429 | 2 |
| #21443926 | 2 |
| #21443925 | 2 |
| C2×C61×#360 | 2 |
| #13001 | 61 |