Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
496 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21456967 | C2 | semidirect |
| 3. #21444501 | C2 | semidirect |
| 4. #21444222 | C2 | semidirect |
| 6. #21443714 | C2 | semidirect |
| 220. C61 | #10190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456967 | 2 |
| C2×#16840042 | 2 |
| #21444501 | 2 |
| #21444222 | 2 |
| #21444140 | 2 |
| #21443714 | 2 |
| C61×#3077 | 2 |
| #10190 | 61 |