Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #21422152 | C2 | semidirect |
| 5. #21422151 | C2 | semidirect |
| 6. #21422150 | C2 | semidirect |
| 7. C59×#1364 | C2 | semidirect |
| 130. #1364 | D59 | semidirect |
| 152. C59 | #11974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D59 | 2 |
| #21425898 | 2 |
| #21422858 | 2 |
| #21422152 | 2 |
| #21422151 | 2 |
| #21422150 | 2 |
| C59×#1364 | 2 |
| #11974 | 59 |