Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21448048 | C2 | semidirect |
| 2. #21447869 | C2 | semidirect |
| 4. #21443877 | C2 | semidirect |
| 5. #21443783 | C2 | semidirect |
| 90. D4×C61 | Q32 | semidirect |
| 152. C61 | #12346 | semidirect |
| 220. D4 | #14519723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448048 | 2 |
| #21447869 | 2 |
| #21445184 | 2 |
| #21443877 | 2 |
| #21443783 | 2 |
| D4⋊#11758185 | 2 |
| C61×#3338 | 2 |
| #12346 | 61 |