Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21435408 | C2 | semidirect |
| 2. #21434191 | C2 | semidirect |
| 4. #21424894 | C2 | semidirect |
| 5. #21422706 | C2 | semidirect |
| 6. #21421965 | C2 | semidirect |
| 7. C59×#1531 | C2 | semidirect |
| 205. #1531 | D59 | semidirect |
| 239. C59 | #10027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435408 | 2 |
| #21434191 | 2 |
| #21434188 | 2 |
| #21424894 | 2 |
| #21422706 | 2 |
| #21421965 | 2 |
| C59×#1531 | 2 |
| #10027 | 59 |