Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425429 | C2 | semidirect |
| 3. #21425195 | C2 | semidirect |
| 4. #21421922 | C2 | semidirect |
| 5. #21421919 | C2 | semidirect |
| 226. C59 | #7785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425429 | 2 |
| #21425232 | 2 |
| #21425195 | 2 |
| #21421922 | 2 |
| #21421919 | 2 |
| #21421917 | 2 |
| C59×#2808 | 2 |
| #7785 | 59 |