Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 27. #97×C53 | C8 | semidirect |
| 117. C53 | #7023 | semidirect |
| 130. #97 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274858 | 2 |
| C4×C4⋊#88322 | 2 |
| C53×#1745 | 2 |
| #7023 | 53 |