Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 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. #21426842 | C2 | semidirect |
| 4. #21422778 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 10. #16837775 | C4 | semidirect |
| 11. #16837753 | C4 | semidirect |
| 110. C4×Dic59 | SD16 | semidirect |
| 182. #1286 | D59 | semidirect |
| 209. C59 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435023 | 2 |
| #21426842 | 2 |
| #21424927 | 2 |
| #21422778 | 2 |
| #21422655 | 2 |
| #21421924 | 2 |
| C59×#1286 | 2 |
| #9301 | 59 |