Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. #21425870 | C2 | semidirect |
| 3. #21425823 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. #21425701 | C2 | semidirect |
| 6. #21424994 | C2 | semidirect |
| 7. C59×#1978 | C2 | semidirect |
| 11. C2×#14273671 | C4 | semidirect |
| 12. C2×#14273668 | C4 | semidirect |
| 167. #1978 | D59 | semidirect |
| 194. C59 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21425870 | 2 |
| #21425823 | 2 |
| #21425812 | 2 |
| #21425701 | 2 |
| #21424994 | 2 |
| C59×#1978 | 2 |
| #13247 | 59 |