Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #21433172 | C2 | semidirect |
| 2. #21422604 | C2 | semidirect |
| 3. #21422604 | C2 | semidirect |
| 4. #21422565 | C2 | semidirect |
| 5. #21421958 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 22. C59×#493 | C4 | semidirect |
| 23. C59×#492 | C4 | semidirect |
| 24. C59×#487 | C4 | semidirect |
| 25. C59×#486 | C4 | semidirect |
| 188. #493 | Dic59 | semidirect |
| 189. #492 | Dic59 | semidirect |
| 190. #487 | Dic59 | semidirect |
| 191. #486 | Dic59 | semidirect |
| 207. C59 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433172 | 2 |
| #21422604 | 2 |
| #21422565 | 2 |
| #21421958 | 2 |
| #21421924 | 2 |
| C59×#3207 | 2 |
| #9281 | 59 |