Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 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. C24×#92420 | C2 | semidirect |
| 2. C2×#16840791 | C2 | semidirect |
| 3. #21461794 | C2 | semidirect |
| 4. #21461762 | C2 | semidirect |
| 5. #21461641 | C2 | semidirect |
| 6. #21461556 | C2 | semidirect |
| 8. C22×#11758213 | C22 | semidirect |
| 13. C2×C4⋊#92420 | C22 | semidirect |
| 14. C2×#14519834 | C22 | semidirect |
| 17. C2×#14519832 | C22 | semidirect |
| 18. #16840628 | C22 | semidirect |
| 31. C22×#92420 | D4 | semidirect |
| 60. C24×C61 | M16 | semidirect |
| 129. #92420 | #120 | semidirect |
| 136. C22×C61 | #435 | semidirect |
| 179. C61 | #21440 | semidirect |
| 215. C24 | #11758213 | semidirect |
| 292. C22 | #16840791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#92420 | 2 |
| C2×#16840791 | 2 |
| #21461794 | 2 |
| #21461762 | 2 |
| #21461641 | 2 |
| #21461556 | 2 |
| #21448318 | 2 |
| #21440 | 61 |