Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21425505 | C2 | semidirect |
| 4. #21421922 | C2 | semidirect |
| 5. #21421921 | C2 | semidirect |
| 7. C59×#2072 | C2 | semidirect |
| 188. #2072 | D59 | semidirect |
| 219. C59 | #7821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432040 | 2 |
| #21425625 | 2 |
| #21425505 | 2 |
| #21421922 | 2 |
| #21421921 | 2 |
| #21421916 | 2 |
| C59×#2072 | 2 |
| #7821 | 59 |