Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21433235 | C2 | semidirect |
| 2. #21425024 | C2 | semidirect |
| 3. #21422810 | C2 | semidirect |
| 4. #21422621 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 26. C59×#496 | C4 | semidirect |
| 27. C59×#490 | C4 | semidirect |
| 225. #496 | Dic59 | semidirect |
| 226. #490 | Dic59 | semidirect |
| 248. C59 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433235 | 2 |
| #21425024 | 2 |
| #21422810 | 2 |
| #21422621 | 2 |
| #21421965 | 2 |
| #21421951 | 2 |
| C59×#3217 | 2 |
| #9378 | 59 |