Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #21433228 | C2 | semidirect |
| 2. #21422831 | C2 | semidirect |
| 3. #21422764 | C2 | semidirect |
| 4. #21422758 | C2 | semidirect |
| 8. #16837455 | C22 | semidirect |
| 9. #16837426 | C22 | semidirect |
| 10. #16837151 | C22 | semidirect |
| 11. #16837151 | C22 | semidirect |
| 12. #16837146 | C22 | semidirect |
| 13. #16837146 | C22 | semidirect |
| 137. C59 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433228 | 2 |
| #21422831 | 2 |
| #21422764 | 2 |
| #21422758 | 2 |
| C59×#3498 | 2 |
| #17782 | 59 |