Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20290922 | C2 | semidirect |
| 3. C4×#13133285 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 9. #16811539 | C4 | semidirect |
| 15. C4×Dic212 | C4 | semidirect |
| 16. #16810717 | C4 | semidirect |
| 19. D8×Dic53 | C4 | semidirect |
| 23. C4×D8×C53 | C4 | semidirect |
| 27. #13133292 | C2×C4 | semidirect |
| 30. #13133285 | C2×C4 | semidirect |
| 77. D8×C53 | C42 | semidirect |
| 98. Dic212 | C42 | semidirect |
| 151. Dic53 | #360 | semidirect |
| 171. C4×D8 | #6157 | semidirect |
| 181. C53 | C4×#360 | semidirect |
| 235. D8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811539 | 2 |
| #20290922 | 2 |
| C4×#13133285 | 2 |
| #20289786 | 2 |
| C4×#13133236 | 2 |
| C4×#360 | 53 |