Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #21425870 | C2 | semidirect |
| 3. #21425843 | C2 | semidirect |
| 4. #21425823 | C2 | semidirect |
| 5. #21425707 | C2 | semidirect |
| 6. #21422210 | C2 | semidirect |
| 7. C59×#1810 | C2 | semidirect |
| 46. C2×C59⋊C16 | D4 | semidirect |
| 181. #1810 | D59 | semidirect |
| 208. C59 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| #21425870 | 2 |
| #21425843 | 2 |
| #21425823 | 2 |
| #21425707 | 2 |
| #21422210 | 2 |
| C59×#1810 | 2 |
| #13395 | 59 |