Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21425912 | C2 | semidirect |
| 3. #21422089 | C2 | semidirect |
| 5. #21422083 | C2 | semidirect |
| 7. C59×#1747 | C2 | semidirect |
| 9. #16837800 | C4 | semidirect |
| 10. #16837786 | C4 | semidirect |
| 15. #16837515 | C4 | semidirect |
| 16. #16837510 | C4 | semidirect |
| 143. #1747 | D59 | semidirect |
| 171. C59 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434713 | 2 |
| #21425912 | 2 |
| #21422089 | 2 |
| #21422086 | 2 |
| #21422083 | 2 |
| #21422080 | 2 |
| C59×#1747 | 2 |
| #11769 | 59 |