Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20277027 | C2 | semidirect |
| 2. #20276818 | C2 | semidirect |
| 3. #20272902 | C2 | semidirect |
| 4. #20272855 | C2 | semidirect |
| 5. C53×#3414 | C2 | semidirect |
| 6. C2×D848 | C22 | semidirect |
| 10. #16810457 | C22 | semidirect |
| 11. #16810451 | C22 | semidirect |
| 35. Q32×C53 | D4 | semidirect |
| 39. D16×C53 | D4 | semidirect |
| 107. #3414 | D53 | semidirect |
| 130. C53 | #13667 | semidirect |
| 143. Q32 | C22⋊D53 | semidirect |
| 148. D16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277027 | 2 |
| #20276818 | 2 |
| #20272902 | 2 |
| #20272855 | 2 |
| C53×#3414 | 2 |
| #13667 | 53 |