Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
666 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276326 | C2 | semidirect |
| 3. #20272638 | C2 | semidirect |
| 4. C53×#2112 | C2 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 19. C53×C22⋊C16 | C22 | semidirect |
| 115. C22×D53 | M32 | semidirect |
| 170. #2112 | D53 | semidirect |
| 193. C22⋊C16 | C2×D53 | semidirect |
| 194. C53 | #11418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133129 | 2 |
| #20276326 | 2 |
| #20272638 | 2 |
| C53×#2112 | 2 |
| #11418 | 53 |