Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21434214 | C2 | semidirect |
| 3. #21429579 | C2 | semidirect |
| 4. #21422693 | C2 | semidirect |
| 5. #21422544 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1980 | C2 | semidirect |
| 213. #1980 | D59 | semidirect |
| 249. C59 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435079 | 2 |
| #21434214 | 2 |
| #21429579 | 2 |
| #21422693 | 2 |
| #21422544 | 2 |
| #21421952 | 2 |
| C59×#1980 | 2 |
| #10006 | 59 |