Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 159 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. #21426343 | C2 | semidirect |
| 4. #21426342 | C2 | semidirect |
| 5. #21426341 | C2 | semidirect |
| 6. #21426340 | C2 | semidirect |
| 9. C59×#2245 | C2 | semidirect |
| 149. #2245 | D59 | direct (N × H) |
| 154. D59 | #2245 | direct (N × H) |
| 180. C59 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D59 | 2 |
| #494×D59 | 2 |
| #21426343 | 2 |
| #21426342 | 2 |
| #21426341 | 2 |
| #21426340 | 2 |
| #358×D59 | 2 |
| #346×D59 | 2 |
| C59×#2245 | 2 |
| C2×#2245 | 59 |