Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21434222 | C2 | semidirect |
| 3. #21425041 | C2 | semidirect |
| 5. #21422542 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 238. C59 | #10010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434222 | 2 |
| #21429585 | 2 |
| #21425041 | 2 |
| #21422694 | 2 |
| #21422542 | 2 |
| #21421953 | 2 |
| C59×#3215 | 2 |
| #10010 | 59 |