Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425085 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 6. C59⋊#1309 | C2 | semidirect |
| 7. C59×#1299 | C2 | semidirect |
| 187. #1299 | D59 | semidirect |
| 216. C59 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433584 | 2 |
| #21433217 | 2 |
| #21425085 | 2 |
| #21422776 | 2 |
| #21422536 | 2 |
| C59⋊#1309 | 2 |
| C59×#1299 | 2 |
| #9353 | 59 |