Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. #20291048 | C2 | semidirect |
| 2. C4×#13133292 | C2 | semidirect |
| 3. #20289666 | C2 | semidirect |
| 4. D4⋊#11719910 | C2 | semidirect |
| 9. C4⋊#11719910 | C22 | semidirect |
| 11. C4×#11719910 | C22 | semidirect |
| 110. D4×C53 | M32 | semidirect |
| 124. D212 | M32 | semidirect |
| 191. C53 | #11583 | semidirect |
| 282. D4 | #13133292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291048 | 2 |
| C4×#13133292 | 2 |
| #20289666 | 2 |
| D4⋊#11719910 | 2 |
| C8×D4×D53 | 2 |
| #11583 | 53 |