Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21434642 | C2 | semidirect |
| 4. #21422814 | C2 | semidirect |
| 6. #21422607 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 186. #1300 | D59 | semidirect |
| 215. C59 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435101 | 2 |
| #21434642 | 2 |
| #21430206 | 2 |
| #21422814 | 2 |
| #21422693 | 2 |
| #21422607 | 2 |
| C59×#1300 | 2 |
| #10102 | 59 |