Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
402 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #21425869 | C2 | semidirect |
| 4. #21422211 | C2 | semidirect |
| 17. C59×#349 | C4 | semidirect |
| 42. M32×C59 | C2×C4 | semidirect |
| 136. #349 | Dic59 | semidirect |
| 138. C59 | #12932 | semidirect |
| 156. M32 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432686 | 2 |
| #21425869 | 2 |
| #21424138 | 2 |
| #21422211 | 2 |
| C2×C59×#349 | 2 |
| #12932 | 59 |