Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21425854 | C2 | semidirect |
| 4. #21424219 | C2 | semidirect |
| 5. #21422212 | C2 | semidirect |
| 6. #21422190 | C2 | semidirect |
| 10. #16837524 | C4 | semidirect |
| 168. C59 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433013 | 2 |
| #21425854 | 2 |
| #21425845 | 2 |
| #21424219 | 2 |
| #21422212 | 2 |
| #21422190 | 2 |
| C59×#2138 | 2 |
| #12829 | 59 |