Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. #16837178 | C4 | semidirect |
| 13. C4×C59⋊C16 | C4 | semidirect |
| 126. C59 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425693 | 2 |
| #21424220 | 2 |
| #21422199 | 2 |
| #21422197 | 2 |
| #21422193 | 2 |
| #21422191 | 2 |
| C59×#1833 | 2 |
| #12893 | 59 |