Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #21434674 | C2 | semidirect |
| 2. #21434673 | C2 | semidirect |
| 3. #21434523 | C2 | semidirect |
| 4. #21434519 | C2 | semidirect |
| 5. #21423769 | C2 | semidirect |
| 6. #21423767 | C2 | semidirect |
| 7. #21423765 | C2 | semidirect |
| 8. #21423763 | C2 | semidirect |
| 9. #21423761 | C2 | semidirect |
| 10. #322×D59 | C2 | semidirect |
| 11. C59×#1721 | C2 | semidirect |
| 135. C8×D59 | D8 | semidirect |
| 196. #1721 | D59 | semidirect |
| 235. C59 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434674 | 2 |
| #21434673 | 2 |
| #21434523 | 2 |
| #21434519 | 2 |
| #21423769 | 2 |
| #21423767 | 2 |
| #21423765 | 2 |
| #21423763 | 2 |
| #21423761 | 2 |
| #322×D59 | 2 |
| C59×#1721 | 2 |
| #19616 | 59 |