Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20276940 | C2 | semidirect |
| 3. #20276849 | C2 | semidirect |
| 4. #20272760 | C2 | semidirect |
| 5. #20272675 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 7. C53×#1673 | C2 | semidirect |
| 16. C4⋊#11719908 | C22 | semidirect |
| 19. C4×#11719908 | C22 | semidirect |
| 20. C53×#500 | C22 | semidirect |
| 23. C53×#335 | C22 | semidirect |
| 89. D424 | SD16 | semidirect |
| 149. #1673 | D53 | semidirect |
| 161. #500 | C2×D53 | semidirect |
| 174. #335 | C2×D53 | semidirect |
| 176. C53 | #12368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D424 | 2 |
| #20276940 | 2 |
| #20276849 | 2 |
| #20272760 | 2 |
| #20272675 | 2 |
| D4⋊#11719908 | 2 |
| C53×#1673 | 2 |
| #12368 | 53 |