Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 5. C2×#13133284 | C4 | semidirect |
| 6. C2×C4⋊#88324 | C4 | semidirect |
| 9. #16811469 | C4 | semidirect |
| 171. C53 | #7252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290573 | 2 |
| #20289947 | 2 |
| #20274446 | 2 |
| #7252 | 53 |