Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21424842 | C2 | semidirect |
| 5. #21422197 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C59×#2155 | C2 | semidirect |
| 20. #16837213 | C4 | semidirect |
| 46. #14273659 | C2×C4 | semidirect |
| 56. M32×C59 | C2×C4 | semidirect |
| 151. #2155 | D59 | semidirect |
| 180. C59 | #12951 | semidirect |
| 203. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432867 | 2 |
| #21425843 | 2 |
| #21425833 | 2 |
| #21424842 | 2 |
| #21422197 | 2 |
| #21422177 | 2 |
| C59×#2155 | 2 |
| #12951 | 59 |