Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 90 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. #16811501 | C4 | semidirect |
| 9. #16811467 | C4 | semidirect |
| 13. C2×#13133124 | C4 | semidirect |
| 14. C22×C4⋊C4×C53 | C4 | semidirect |
| 267. C22×C4⋊C4 | #6157 | semidirect |
| 278. C53 | #7250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811501 | 2 |
| C2×#16811467 | 2 |
| #20272957 | 2 |
| #7250 | 53 |