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. #21422647 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421960 | C2 | semidirect |
| 7. C59×#1515 | C2 | semidirect |
| 10. #16837750 | C4 | semidirect |
| 11. #16837750 | C4 | semidirect |
| 43. C4×C59⋊C8 | C2×C4 | semidirect |
| 47. C4⋊Q8×C59 | C2×C4 | semidirect |
| 48. C4⋊Q8×C59 | C2×C4 | semidirect |
| 167. #1515 | D59 | semidirect |
| 192. C59 | #9425 | semidirect |
| 198. C4⋊Q8 | C4×D59 | semidirect |
| 199. C4⋊Q8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434472 | 2 |
| #21427272 | 2 |
| #21422809 | 2 |
| #21422647 | 2 |
| #21421962 | 2 |
| #21421960 | 2 |
| C59×#1515 | 2 |
| #9425 | 59 |