Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1250 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 344 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 |
|---|---|---|
| 2. #20290452 | C2 | semidirect |
| 3. C22⋊C4×#88324 | C2 | semidirect |
| 4. #20290445 | C2 | semidirect |
| 7. C2×C22⋊#88324 | C4 | semidirect |
| 11. C2×#13133272 | C22 | semidirect |
| 12. C2×C4×#88324 | C22 | semidirect |
| 13. #16811489 | C22 | semidirect |
| 147. C53 | #20528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#88324 | 2 |
| #20290452 | 2 |
| C22⋊C4×#88324 | 2 |
| #20290445 | 2 |
| #20277093 | 2 |
| #20528 | 53 |