Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
308 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21448062 | C2 | semidirect |
| 3. #21445303 | C2 | semidirect |
| 4. #21443871 | C2 | semidirect |
| 5. #21443801 | C2 | semidirect |
| 6. #21443786 | C2 | semidirect |
| 7. C61×#3389 | C2 | semidirect |
| 71. D8×C61 | SD16 | semidirect |
| 141. #3389 | D61 | semidirect |
| 172. C61 | #12360 | semidirect |
| 221. D8 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448062 | 2 |
| #21447854 | 2 |
| #21445303 | 2 |
| #21443871 | 2 |
| #21443801 | 2 |
| #21443786 | 2 |
| C61×#3389 | 2 |
| #12360 | 61 |