Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 23. #16839511 | C4 | semidirect |
| 24. #16839509 | C4 | semidirect |
| 25. #16839507 | C4 | semidirect |
| 26. C61×#333 | C4 | semidirect |
| 172. #333 | #6923 | semidirect |
| 179. C61 | #9591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461994 | 2 |
| #21461933 | 2 |
| #21461169 | 2 |
| #21461031 | 2 |
| #21460716 | 2 |
| #21460653 | 2 |
| #21444473 | 2 |
| #9591 | 61 |