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. #21434218 | C2 | semidirect |
| 3. #21429584 | C2 | semidirect |
| 4. #21425015 | C2 | semidirect |
| 5. #21422693 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1491 | C2 | semidirect |
| 215. #1491 | 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 |
|---|---|
| #21435085 | 2 |
| #21434218 | 2 |
| #21429584 | 2 |
| #21425015 | 2 |
| #21422693 | 2 |
| #21421953 | 2 |
| C59×#1491 | 2 |
| #10006 | 59 |