Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462003 | C2 | semidirect |
| 3. #21461333 | C2 | semidirect |
| 5. #21460673 | C2 | semidirect |
| 6. #21460644 | C2 | semidirect |
| 22. #16840158 | C4 | semidirect |
| 23. #16840110 | C4 | semidirect |
| 24. #16840109 | C4 | semidirect |
| 28. C61×#498 | C4 | semidirect |
| 199. #498 | #6923 | semidirect |
| 216. C61 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462546 | 2 |
| #21462003 | 2 |
| #21461333 | 2 |
| #21461250 | 2 |
| #21460673 | 2 |
| #21460644 | 2 |
| #21456948 | 2 |
| #9287 | 61 |