Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #16837804 | C4 | semidirect |
| 11. #16837800 | C4 | semidirect |
| 49. M32×C59 | Q8 | semidirect |
| 51. C2×C16×C59 | Q8 | semidirect |
| 146. C59 | #13291 | semidirect |
| 162. M32 | Dic118 | semidirect |
| 164. C2×C16 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434627 | 2 |
| #21424220 | 2 |
| #21422211 | 2 |
| #21422202 | 2 |
| #21422198 | 2 |
| #21422195 | 2 |
| C59×#2110 | 2 |
| #13291 | 59 |