Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
266 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 100 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. C4⋊#11719910 | C4 | semidirect |
| 8. #16811511 | C4 | semidirect |
| 119. C53 | #7169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291047 | 2 |
| C4×#13133291 | 2 |
| C4⋊C4×#88322 | 2 |
| #7169 | 53 |