Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21425905 | C2 | semidirect |
| 3. #21424243 | C2 | semidirect |
| 4. #21422088 | C2 | semidirect |
| 5. #21422087 | C2 | semidirect |
| 6. #21422080 | C2 | semidirect |
| 7. C59×#1339 | C2 | semidirect |
| 9. #16837799 | C4 | semidirect |
| 10. #16837777 | C4 | semidirect |
| 14. #16837514 | C4 | semidirect |
| 15. #16837513 | C4 | semidirect |
| 150. #1339 | D59 | semidirect |
| 175. C59 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434829 | 2 |
| #21425905 | 2 |
| #21424243 | 2 |
| #21422088 | 2 |
| #21422087 | 2 |
| #21422080 | 2 |
| C59×#1339 | 2 |
| #11837 | 59 |