Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
808 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #21423424 | C2 | semidirect |
| 4. #21423398 | C2 | semidirect |
| 5. #21422723 | C2 | semidirect |
| 6. #21422698 | C2 | semidirect |
| 7. C2×C59×#564 | C2 | semidirect |
| 143. C2×#564 | D59 | semidirect |
| 176. C59 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435286 | 2 |
| #21434499 | 2 |
| #21423424 | 2 |
| #21423398 | 2 |
| #21422723 | 2 |
| #21422698 | 2 |
| C2×C59×#564 | 2 |
| #19003 | 59 |