Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20277440 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20273275 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272544 | C2 | semidirect |
| 7. C53×#1963 | C2 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 48. C4×#88322 | C2×C4 | semidirect |
| 53. C4⋊Q8×C53 | C2×C4 | semidirect |
| 54. #127×C53 | C2×C4 | semidirect |
| 111. C42×C53 | D8 | semidirect |
| 207. #1963 | D53 | semidirect |
| 238. C53 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D53 | semidirect |
| 251. #127 | C4×D53 | semidirect |
| 331. C42 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20277440 | 2 |
| #20273384 | 2 |
| #20273275 | 2 |
| #20272575 | 2 |
| #20272544 | 2 |
| C53×#1963 | 2 |
| #9299 | 53 |