Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21448048 | C2 | semidirect |
| 3. #21445189 | C2 | semidirect |
| 4. #21443874 | C2 | semidirect |
| 5. Q8⋊#11758185 | C2 | semidirect |
| 90. Q8×C61 | SD32 | semidirect |
| 154. C61 | #12356 | semidirect |
| 222. Q8 | #14519721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448048 | 2 |
| #21447864 | 2 |
| #21445189 | 2 |
| #21443874 | 2 |
| Q8⋊#11758185 | 2 |
| #21443780 | 2 |
| Q8×D8×C61 | 2 |
| #12356 | 61 |