Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20277441 | C2 | semidirect |
| 3. #20275546 | C2 | semidirect |
| 4. #20273276 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810969 | C4 | semidirect |
| 30. #13133217 | C2×C4 | semidirect |
| 31. #13133214 | C2×C4 | semidirect |
| 50. C4×#88322 | C2×C4 | semidirect |
| 122. C4×Dic53 | D8 | semidirect |
| 208. #1545 | D53 | semidirect |
| 238. C53 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285633 | 2 |
| #20277441 | 2 |
| #20275546 | 2 |
| #20273276 | 2 |
| #20272575 | 2 |
| #20272543 | 2 |
| C53×#1545 | 2 |
| #9299 | 53 |