Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 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. #21425020 | C2 | semidirect |
| 3. #21422813 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 26. C59×#501 | C4 | semidirect |
| 27. C59×#489 | C4 | semidirect |
| 204. #501 | Dic59 | semidirect |
| 205. #489 | Dic59 | semidirect |
| 227. C59 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433235 | 2 |
| #21425020 | 2 |
| #21422813 | 2 |
| #21422621 | 2 |
| #21421965 | 2 |
| #21421951 | 2 |
| C59×#3239 | 2 |
| #9377 | 59 |