Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21423693 | C2 | semidirect |
| 4. #21422160 | C2 | semidirect |
| 5. #21422155 | C2 | semidirect |
| 6. #21422144 | C2 | semidirect |
| 88. C8×C59 | SD32 | semidirect |
| 130. C59 | #12420 | semidirect |
| 196. C8 | #14273671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426243 | 2 |
| #21426141 | 2 |
| #21423693 | 2 |
| #21422160 | 2 |
| #21422155 | 2 |
| #21422144 | 2 |
| C8×D8×C59 | 2 |
| #12420 | 59 |