Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
610 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21446658 | C2 | semidirect |
| 3. #21444488 | C2 | semidirect |
| 4. C8×#11758194 | C2 | semidirect |
| 5. C61×#1567 | C2 | semidirect |
| 69. #11758194 | D8 | semidirect |
| 98. C8×C61 | #100 | semidirect |
| 119. #1567 | D61 | semidirect |
| 141. C61 | #9802 | semidirect |
| 222. C8 | #14519693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840139 | 2 |
| #21446658 | 2 |
| #21444488 | 2 |
| C8×#11758194 | 2 |
| C61×#1567 | 2 |
| #9802 | 61 |