Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21426456 | C2 | semidirect |
| 3. #21425014 | C2 | semidirect |
| 4. #21422605 | C2 | semidirect |
| 5. #21422538 | C2 | semidirect |
| 6. #21421988 | C2 | semidirect |
| 7. C59×#1285 | C2 | semidirect |
| 12. #16837693 | C4 | semidirect |
| 13. #16837598 | C4 | semidirect |
| 35. #14273727 | C2×C4 | semidirect |
| 36. #14273724 | C2×C4 | semidirect |
| 66. C4⋊C8×C59 | C2×C4 | semidirect |
| 156. D236 | #104 | semidirect |
| 196. #1285 | D59 | semidirect |
| 225. C59 | #9325 | semidirect |
| 254. C4⋊C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434188 | 2 |
| #21426456 | 2 |
| #21425014 | 2 |
| #21422605 | 2 |
| #21422538 | 2 |
| #21421988 | 2 |
| C59×#1285 | 2 |
| #9325 | 59 |