Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 7. #16837199 | C4 | semidirect |
| 9. #16837146 | C4 | semidirect |
| 135. C59 | #7496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425781 | 2 |
| #21422831 | 2 |
| C59×#1884 | 2 |
| #7496 | 59 |