Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 1. #21429321 | C2 | semidirect |
| 5. #21421974 | C2 | semidirect |
| 6. #21421942 | C2 | semidirect |
| 7. C59×#1289 | C2 | semidirect |
| 218. #1289 | D59 | semidirect |
| 249. C59 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429321 | 2 |
| #21424931 | 2 |
| #21422663 | 2 |
| C2×#16837137 | 2 |
| #21421974 | 2 |
| #21421942 | 2 |
| C59×#1289 | 2 |
| #10376 | 59 |