Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 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. #21434643 | C2 | semidirect |
| 3. #21422812 | C2 | semidirect |
| 5. #21422608 | C2 | semidirect |
| 6. #21421988 | C2 | semidirect |
| 210. C59 | #10100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434643 | 2 |
| #21430036 | 2 |
| #21422812 | 2 |
| #21422694 | 2 |
| #21422608 | 2 |
| #21421988 | 2 |
| C59×#3215 | 2 |
| #10100 | 59 |