Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 21. #16837200 | C4 | semidirect |
| 221. C59 | #12973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427184 | 2 |
| C2×#16837200 | 2 |
| #21424487 | 2 |
| #21424313 | 2 |
| #21424310 | 2 |
| #21422222 | 2 |
| C59×#1394 | 2 |
| #12973 | 59 |