Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 6. #16840603 | C4 | semidirect |
| 7. C8×#92420 | C4 | semidirect |
| 23. #14519687 | C8 | semidirect |
| 32. #97×C61 | C8 | semidirect |
| 106. C61 | #8138 | semidirect |
| 118. #97 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461022 | 2 |
| #21460645 | 2 |
| #21460643 | 2 |
| #21445507 | 2 |
| #8138 | 61 |