Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
936 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#16810432 | C2 | semidirect |
| 3. #20276425 | C2 | semidirect |
| 4. C2×#16810405 | C2 | semidirect |
| 5. C53×#1809 | C2 | semidirect |
| 9. #16811423 | C4 | semidirect |
| 14. C2×#13133157 | C22 | semidirect |
| 20. C2×#107×C53 | C22 | semidirect |
| 21. C2×#106×C53 | C22 | semidirect |
| 123. Dic212 | C22⋊C4 | semidirect |
| 126. D424 | C22⋊C4 | semidirect |
| 204. #1809 | D53 | semidirect |
| 222. C2×#107 | C2×D53 | semidirect |
| 223. C2×#106 | C2×D53 | semidirect |
| 230. C53 | #12739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811423 | 2 |
| C2×#16810432 | 2 |
| #20276425 | 2 |
| C2×#16810405 | 2 |
| C53×#1809 | 2 |
| #12739 | 53 |