Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #21425850 | C2 | semidirect |
| 3. #346×D59 | C2 | semidirect |
| 4. #21422055 | C2 | semidirect |
| 5. #21422054 | C2 | semidirect |
| 6. #21422053 | C2 | semidirect |
| 7. C59×#1330 | C2 | semidirect |
| 168. #1330 | D59 | semidirect |
| 194. C59 | #11588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432805 | 2 |
| #21425850 | 2 |
| #346×D59 | 2 |
| #21422055 | 2 |
| #21422054 | 2 |
| #21422053 | 2 |
| C59×#1330 | 2 |
| #11588 | 59 |