Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1314 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×#11758217 | C2 | semidirect |
| 2. #21461961 | C2 | semidirect |
| 3. #21461683 | C2 | semidirect |
| 4. C4×#14519837 | C2 | semidirect |
| 94. #11758217 | #41 | semidirect |
| 116. Q8×C61 | #100 | semidirect |
| 195. C61 | #22536 | semidirect |
| 289. Q8 | #14519837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758217 | 2 |
| #21461961 | 2 |
| #21461683 | 2 |
| C4×#14519837 | 2 |
| C2×#16840431 | 2 |
| #22536 | 61 |