Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 8. #16811469 | C4 | semidirect |
| 11. C2×C4⋊#88322 | C4 | semidirect |
| 14. C2×C4⋊C8×C53 | C4 | semidirect |
| 154. C2×C4⋊C8 | #6157 | semidirect |
| 161. C53 | #7252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290414 | 2 |
| #20289948 | 2 |
| #20274696 | 2 |
| #7252 | 53 |