Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
844 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 94 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×(C2×#6157)⋊C4 | C4 | semidirect |
| 7. C2×C22⋊#88322 | C4 | semidirect |
| 9. C2×C22⋊C8×C53 | C4 | semidirect |
| 164. C2×C22⋊C8 | #6157 | semidirect |
| 167. C53 | #7035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289889 | 2 |
| #20274624 | 2 |
| #7035 | 53 |