Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21425361 | C2 | semidirect |
| 4. #21422114 | C2 | semidirect |
| 6. #21422037 | C2 | semidirect |
| 7. C59×#2188 | C2 | semidirect |
| 156. #2188 | D59 | semidirect |
| 186. C59 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435558 | 2 |
| #21426013 | 2 |
| #21425361 | 2 |
| #21422114 | 2 |
| #21422112 | 2 |
| #21422037 | 2 |
| C59×#2188 | 2 |
| #12169 | 59 |