Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21456824 | C2 | semidirect |
| 3. #21456368 | C2 | semidirect |
| 4. #21445138 | C2 | semidirect |
| 5. #21444418 | C2 | semidirect |
| 6. C61×#1534 | C2 | semidirect |
| 15. #16840172 | C22 | semidirect |
| 17. #16840156 | C22 | semidirect |
| 18. #16840122 | C22 | semidirect |
| 24. #16839501 | C22 | semidirect |
| 27. C61×#330 | C22 | semidirect |
| 152. #1534 | D61 | semidirect |
| 177. #330 | C2×D61 | semidirect |
| 179. C61 | #19006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840510 | 2 |
| #21456824 | 2 |
| #21456368 | 2 |
| #21445138 | 2 |
| #21444418 | 2 |
| C61×#1534 | 2 |
| #19006 | 61 |