Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1124 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#16811064 | C2 | semidirect |
| 3. #20276649 | C2 | semidirect |
| 4. #20276632 | C2 | semidirect |
| 5. #20276435 | C2 | semidirect |
| 6. #20276326 | C2 | semidirect |
| 7. C23×Q16×C53 | C2 | semidirect |
| 11. C2×#13133163 | C22 | semidirect |
| 12. C2×#13133160 | C22 | semidirect |
| 19. #16810427 | C22 | semidirect |
| 61. C2×Q16×C53 | D4 | semidirect |
| 154. C22×C53 | #510 | semidirect |
| 165. C23×Q16 | D53 | semidirect |
| 197. C53 | #33518 | semidirect |
| 215. C2×Q16 | C22⋊D53 | semidirect |
| 325. C22 | #16811064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20284296 | 2 |
| #20276649 | 2 |
| #20276632 | 2 |
| #20276435 | 2 |
| #20276326 | 2 |
| C23×Q16×C53 | 2 |
| #33518 | 53 |