Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
496 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21435249 | C2 | semidirect |
| 4. #21422778 | C2 | semidirect |
| 5. #21422498 | C2 | semidirect |
| 7. C59×#1301 | C2 | semidirect |
| 190. #1301 | D59 | semidirect |
| 220. C59 | #10190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435249 | 2 |
| #21433895 | 2 |
| C2×#16837683 | 2 |
| #21422778 | 2 |
| #21422498 | 2 |
| #21422416 | 2 |
| C59×#1301 | 2 |
| #10190 | 59 |