Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21454411 | C2 | semidirect |
| 3. C2×#16839572 | C2 | semidirect |
| 4. #21447448 | C2 | semidirect |
| 5. #21443935 | C2 | semidirect |
| 6. #21443918 | C2 | semidirect |
| 7. C61×#2145 | C2 | semidirect |
| 12. #16840034 | C4 | semidirect |
| 13. #16840029 | C4 | semidirect |
| 53. #14519713 | C2×C4 | semidirect |
| 65. C2×Q16×C61 | C2×C4 | semidirect |
| 67. C2×D8×C61 | C2×C4 | semidirect |
| 190. #2145 | D61 | semidirect |
| 222. C61 | #13005 | semidirect |
| 234. C2×Q16 | C4×D61 | semidirect |
| 236. C2×D8 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455535 | 2 |
| #21454411 | 2 |
| C2×#16839572 | 2 |
| #21447448 | 2 |
| #21443935 | 2 |
| #21443918 | 2 |
| C61×#2145 | 2 |
| #13005 | 61 |