Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
480 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. #21432964 | C2 | semidirect |
| 5. #21422193 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 7. C2×C59×#362 | C2 | semidirect |
| 12. C2×#14273670 | C4 | semidirect |
| 157. C2×#362 | D59 | semidirect |
| 185. C59 | #13018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273670 | 2 |
| #21432964 | 2 |
| #21425813 | 2 |
| #21425004 | 2 |
| #21422193 | 2 |
| #21422186 | 2 |
| C2×C59×#362 | 2 |
| #13018 | 59 |