Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
812 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21454264 | C2 | semidirect |
| 2. #21445747 | C2 | semidirect |
| 3. #21444146 | C2 | semidirect |
| 4. #21443727 | C2 | semidirect |
| 37. C22⋊#92418 | D4 | semidirect |
| 275. C61 | #9511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454264 | 2 |
| #21445747 | 2 |
| #21444146 | 2 |
| #21443727 | 2 |
| C61×#2404 | 2 |
| #9511 | 61 |