Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #21425693 | C2 | semidirect |
| 5. #21422210 | C2 | semidirect |
| 6. #21422193 | C2 | semidirect |
| 7. C59×#1953 | C2 | semidirect |
| 14. #16837217 | C4 | semidirect |
| 15. #16837214 | C4 | semidirect |
| 140. #1953 | D59 | semidirect |
| 165. C59 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425843 | 2 |
| C2×#16837208 | 2 |
| #21425693 | 2 |
| #21424994 | 2 |
| #21422210 | 2 |
| #21422193 | 2 |
| C59×#1953 | 2 |
| #13146 | 59 |