Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21424226 | C2 | semidirect |
| 3. #21422842 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 11. #16837479 | C4 | semidirect |
| 13. #16837467 | C4 | semidirect |
| 169. #1286 | D59 | semidirect |
| 195. C59 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432807 | 2 |
| #21424226 | 2 |
| #21422842 | 2 |
| #21422657 | 2 |
| #21422655 | 2 |
| #21421956 | 2 |
| C59×#1286 | 2 |
| #8678 | 59 |