Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 572 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. #20276326 | C2 | semidirect |
| 4. #20272822 | C2 | semidirect |
| 5. C22×#106×C53 | C2 | semidirect |
| 9. #16810864 | C4 | semidirect |
| 10. #16810859 | C4 | semidirect |
| 24. C2×Dic212 | C2×C4 | semidirect |
| 26. C2×D424 | C2×C4 | semidirect |
| 36. #13133151 | C2×C4 | semidirect |
| 54. #106×C53 | D4 | semidirect |
| 140. C22×C53 | #360 | semidirect |
| 155. C22×#106 | D53 | semidirect |
| 180. C53 | #13001 | semidirect |
| 212. #106 | C22⋊D53 | semidirect |
| 301. C22 | #16810432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| C2×#16810432 | 2 |
| #20276326 | 2 |
| #20272822 | 2 |
| C22×#106×C53 | 2 |
| #13001 | 53 |