Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21422884 | C2 | semidirect |
| 5. #21421987 | C2 | semidirect |
| 6. #21421933 | C2 | semidirect |
| 7. C59×#1452 | C2 | semidirect |
| 143. #1452 | D59 | semidirect |
| 168. C59 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422884 | 2 |
| #21422756 | 2 |
| #21422548 | 2 |
| #21422512 | 2 |
| #21421987 | 2 |
| #21421933 | 2 |
| C59×#1452 | 2 |
| #9588 | 59 |