Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275633 | C2 | semidirect |
| 3. #20273222 | C2 | semidirect |
| 4. #20273158 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#2275 | C2 | semidirect |
| 10. #16810913 | C4 | semidirect |
| 11. #16810818 | C4 | semidirect |
| 32. #13133217 | C2×C4 | semidirect |
| 33. #13133214 | C2×C4 | semidirect |
| 41. C4⋊#88322 | C2×C4 | semidirect |
| 129. D4×C53 | #104 | semidirect |
| 191. #2275 | D53 | semidirect |
| 225. C53 | #9325 | semidirect |
| 332. D4 | #13133145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284806 | 2 |
| #20275633 | 2 |
| #20273222 | 2 |
| #20273158 | 2 |
| #20272608 | 2 |
| #20272571 | 2 |
| C53×#2275 | 2 |
| #9325 | 53 |