Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21444582 | C2 | semidirect |
| 3. #21444420 | C2 | semidirect |
| 5. #21444174 | C2 | semidirect |
| 7. C61×#1451 | C2 | semidirect |
| 176. #1451 | D61 | semidirect |
| 205. C61 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840117 | 2 |
| #21444582 | 2 |
| #21444420 | 2 |
| #21444416 | 2 |
| #21444174 | 2 |
| #21444170 | 2 |
| C61×#1451 | 2 |
| #9790 | 61 |