Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #21425049 | C2 | semidirect |
| 3. #21422822 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 26. C59×#501 | C4 | semidirect |
| 27. C59×#489 | C4 | semidirect |
| 198. #501 | Dic59 | semidirect |
| 199. #489 | Dic59 | semidirect |
| 221. C59 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433235 | 2 |
| #21425049 | 2 |
| #21422822 | 2 |
| #21422621 | 2 |
| #21421965 | 2 |
| #21421951 | 2 |
| C59×#3238 | 2 |
| #9375 | 59 |