Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21422868 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 7. C59×#1307 | C2 | semidirect |
| 120. #1307 | D59 | semidirect |
| 141. C59 | #10647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422868 | 2 |
| #21422816 | 2 |
| #21422792 | 2 |
| #21422564 | 2 |
| #21421965 | 2 |
| #21421957 | 2 |
| C59×#1307 | 2 |
| #10647 | 59 |