Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #21448086 | C2 | semidirect |
| 2. #21447854 | C2 | semidirect |
| 3. #21445298 | C2 | semidirect |
| 4. #21443862 | C2 | semidirect |
| 5. #21443786 | C2 | semidirect |
| 6. #21443777 | C2 | semidirect |
| 7. C61×#3273 | C2 | semidirect |
| 11. #16840139 | C22 | semidirect |
| 13. C4⋊#11758185 | C22 | semidirect |
| 15. #16839538 | C22 | semidirect |
| 16. #16839513 | C22 | semidirect |
| 90. D8×C61 | D8 | semidirect |
| 173. #3273 | D61 | semidirect |
| 206. C61 | #12324 | semidirect |
| 275. D8 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448086 | 2 |
| #21447854 | 2 |
| #21445298 | 2 |
| #21443862 | 2 |
| #21443786 | 2 |
| #21443777 | 2 |
| C61×#3273 | 2 |
| #12324 | 61 |