Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21422648 | C2 | semidirect |
| 5. #21422646 | C2 | semidirect |
| 6. #21421961 | C2 | semidirect |
| 7. C59×#1288 | C2 | semidirect |
| 11. #16837749 | C4 | semidirect |
| 12. #16837749 | C4 | semidirect |
| 29. #14273727 | C2×C4 | semidirect |
| 30. #14273727 | C2×C4 | semidirect |
| 58. C4×C8×C59 | C2×C4 | semidirect |
| 169. #1288 | D59 | semidirect |
| 192. C59 | #9425 | semidirect |
| 223. C4×C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434471 | 2 |
| #21427272 | 2 |
| #21422809 | 2 |
| #21422648 | 2 |
| #21422646 | 2 |
| #21421961 | 2 |
| C59×#1288 | 2 |
| #9425 | 59 |