Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 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. #21422885 | C2 | semidirect |
| 5. #21422379 | C2 | semidirect |
| 6. #21421986 | C2 | semidirect |
| 7. C59×#1278 | C2 | semidirect |
| 150. #1278 | D59 | semidirect |
| 175. C59 | #9586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422885 | 2 |
| #21422756 | 2 |
| #21422548 | 2 |
| #21422514 | 2 |
| #21422379 | 2 |
| #21421986 | 2 |
| C59×#1278 | 2 |
| #9586 | 59 |