Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#16837509 | C2 | semidirect |
| 2. C2×#16837218 | C2 | semidirect |
| 5. #21422195 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 24. C2×Q32×C59 | C4 | semidirect |
| 25. C2×SD32×C59 | C4 | semidirect |
| 182. C2×Q32 | Dic59 | semidirect |
| 183. C2×SD32 | Dic59 | semidirect |
| 196. C59 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837509 | 2 |
| C2×#16837218 | 2 |
| C2×#16837212 | 2 |
| #21424990 | 2 |
| #21422195 | 2 |
| #21422175 | 2 |
| C2×C59×#510 | 2 |
| #13038 | 59 |