Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21445993 | C2 | semidirect |
| 2. #21444587 | C2 | semidirect |
| 5. #21443717 | C2 | semidirect |
| 6. #21443708 | C2 | semidirect |
| 199. C61 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21445993 | 2 |
| #21444587 | 2 |
| #21444407 | 2 |
| #21444284 | 2 |
| #21443717 | 2 |
| #21443708 | 2 |
| C61×#2995 | 2 |
| #8916 | 61 |