Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21454407 | C2 | semidirect |
| 3. #21447535 | C2 | semidirect |
| 4. C2×#16839543 | C2 | semidirect |
| 5. #21443925 | C2 | semidirect |
| 6. #21443924 | C2 | semidirect |
| 7. C61×#2140 | C2 | semidirect |
| 13. #16840012 | C4 | semidirect |
| 49. #14519711 | D4 | semidirect |
| 53. #14519709 | C2×C4 | semidirect |
| 62. C2×D8×C61 | C2×C4 | semidirect |
| 68. #107×C61 | D4 | semidirect |
| 184. #2140 | D61 | semidirect |
| 212. C61 | #12999 | semidirect |
| 221. C2×D8 | C4×D61 | semidirect |
| 250. #107 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840012 | 2 |
| #21454407 | 2 |
| #21447535 | 2 |
| C2×#16839543 | 2 |
| #21443925 | 2 |
| #21443924 | 2 |
| C61×#2140 | 2 |
| #12999 | 61 |