Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
186 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 22 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 |
|---|---|---|
| 1. #20289847 | C2 | semidirect |
| 5. #16811000 | C4 | semidirect |
| 7. C82×C53 | C4 | semidirect |
| 57. C82 | #6157 | semidirect |
| 58. C53 | #7529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289847 | 2 |
| #20274330 | 2 |
| #7529 | 53 |