Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
806 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21438591 | C2 | semidirect |
| 3. #21423422 | C2 | semidirect |
| 4. #21423397 | C2 | semidirect |
| 5. #21422734 | C2 | semidirect |
| 6. #21422710 | C2 | semidirect |
| 178. C59 | #19063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438591 | 2 |
| #21435290 | 2 |
| #21423422 | 2 |
| #21423397 | 2 |
| #21422734 | 2 |
| #21422710 | 2 |
| C59×#3135 | 2 |
| #19063 | 59 |