Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. #21458794 | C2 | semidirect |
| 2. Q8×D488 | C2 | semidirect |
| 3. #21448043 | C2 | semidirect |
| 4. #21447957 | C2 | semidirect |
| 5. #21447855 | C2 | semidirect |
| 6. C4×D976 | C2 | semidirect |
| 7. Q8×C16×C61 | C2 | semidirect |
| 69. D488 | #41 | semidirect |
| 74. Q8×C61 | D16 | semidirect |
| 111. Q8×C16 | D61 | semidirect |
| 134. C61 | #33925 | semidirect |
| 186. Q8 | D976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458794 | 2 |
| Q8×D488 | 2 |
| #21448043 | 2 |
| #21447957 | 2 |
| #21447855 | 2 |
| C4×D976 | 2 |
| Q8×C16×C61 | 2 |
| #33925 | 61 |