Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
288 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 88. Q8×C61 | Q32 | semidirect |
| 145. C61 | #12358 | semidirect |
| 211. Q8 | #14519723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448048 | 2 |
| #21447869 | 2 |
| #21445189 | 2 |
| #21443877 | 2 |
| Q8⋊#11758185 | 2 |
| #21443783 | 2 |
| Q8×Q16×C61 | 2 |
| #12358 | 61 |