Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
516 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21462004 | C2 | semidirect |
| 3. C4×C8×#6923 | C2 | semidirect |
| 4. #21461374 | C2 | semidirect |
| 5. #21461168 | C2 | semidirect |
| 20. #16840135 | C4 | semidirect |
| 21. #16840114 | C4 | semidirect |
| 22. #16840110 | C4 | semidirect |
| 26. C61×#498 | C4 | semidirect |
| 86. C4×#6923 | SD16 | semidirect |
| 140. C8×C61 | #104 | semidirect |
| 175. #498 | #6923 | semidirect |
| 192. C61 | #9843 | semidirect |
| 307. C8 | #14519842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462004 | 2 |
| #21461952 | 2 |
| C4×C8×#6923 | 2 |
| #21461374 | 2 |
| #21461168 | 2 |
| #21461166 | 2 |
| #21456380 | 2 |
| #9843 | 61 |