Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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. #21434525 | C2 | semidirect |
| 3. #21434523 | C2 | semidirect |
| 4. #21423712 | C2 | semidirect |
| 5. #21423710 | C2 | semidirect |
| 6. #21423702 | C2 | semidirect |
| 7. #21423687 | C2 | semidirect |
| 8. C82×D59 | C2 | semidirect |
| 9. C59×#1709 | C2 | semidirect |
| 99. C8×D59 | D8 | semidirect |
| 124. C59⋊C8 | #135 | semidirect |
| 145. #1709 | D59 | semidirect |
| 176. C59 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434674 | 2 |
| #21434525 | 2 |
| #21434523 | 2 |
| #21423712 | 2 |
| #21423710 | 2 |
| #21423702 | 2 |
| #21423687 | 2 |
| C82×D59 | 2 |
| C59×#1709 | 2 |
| #19603 | 59 |