Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 36. C2×C59⋊C16 | Q8 | semidirect |
| 52. M32×C59 | Q8 | semidirect |
| 55. #108×C59 | Q8 | semidirect |
| 158. C59 | #13456 | semidirect |
| 172. M32 | Dic118 | semidirect |
| 178. #108 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434632 | 2 |
| #21425884 | 2 |
| C2×#16837229 | 2 |
| #21424882 | 2 |
| #21422193 | 2 |
| #21422186 | 2 |
| C59×#1387 | 2 |
| #13456 | 59 |