Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #16837799 | C4 | semidirect |
| 33. #14273661 | Q8 | semidirect |
| 49. #108×C59 | Q8 | semidirect |
| 143. C59 | #13272 | semidirect |
| 162. #108 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837799 | 2 |
| C2×#16837222 | 2 |
| #21423978 | 2 |
| #21422203 | 2 |
| #21422202 | 2 |
| #21422196 | 2 |
| C59×#1383 | 2 |
| #13272 | 59 |