Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 468 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. #21425768 | C2 | semidirect |
| 2. #21425746 | C2 | semidirect |
| 3. #21424142 | C2 | semidirect |
| 4. #21423896 | C2 | semidirect |
| 15. C22×D8×C59 | C4 | semidirect |
| 22. C59×#427 | C4 | semidirect |
| 23. C59×#418 | C4 | semidirect |
| 173. C22×D8 | Dic59 | semidirect |
| 181. #427 | Dic59 | semidirect |
| 182. #418 | Dic59 | semidirect |
| 191. C59 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425768 | 2 |
| #21425746 | 2 |
| #21424142 | 2 |
| #21423896 | 2 |
| C59×#3058 | 2 |
| #13231 | 59 |