Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
640 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #21433120 | C2 | semidirect |
| 3. #21422663 | C2 | semidirect |
| 4. #21421974 | C2 | semidirect |
| 5. C59×#1799 | C2 | semidirect |
| 12. #16837332 | C4 | semidirect |
| 13. #16837327 | C4 | semidirect |
| 14. #16837319 | C4 | semidirect |
| 15. #16837311 | C4 | semidirect |
| 45. C22⋊(C59⋊C8) | D4 | semidirect |
| 212. #1799 | D59 | semidirect |
| 243. C59 | #9384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433120 | 2 |
| #21429052 | 2 |
| #21422663 | 2 |
| #21421974 | 2 |
| C59×#1799 | 2 |
| #9384 | 59 |