Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #21422667 | C2 | semidirect |
| 4. #21421974 | C2 | semidirect |
| 11. #16837341 | C4 | semidirect |
| 12. #16837338 | C4 | semidirect |
| 13. #16837322 | C4 | semidirect |
| 14. #16837314 | C4 | semidirect |
| 220. C59 | #9385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433125 | 2 |
| #21429272 | 2 |
| #21422667 | 2 |
| #21421974 | 2 |
| C59×#1799 | 2 |
| #9385 | 59 |