Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
612 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20290891 | C2 | semidirect |
| 3. #20290107 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810904 | C4 | semidirect |
| 26. #16810903 | C4 | semidirect |
| 27. #16810825 | C4 | semidirect |
| 32. C53×#461 | C4 | semidirect |
| 55. #13133217 | C2×C4 | semidirect |
| 72. C4⋊#88322 | C2×C4 | semidirect |
| 79. C4⋊Q8×C53 | C2×C4 | semidirect |
| 81. C4⋊C8×C53 | C2×C4 | semidirect |
| 238. #461 | #6157 | semidirect |
| 256. C53 | #9323 | semidirect |
| 264. C4⋊Q8 | C2×#6157 | semidirect |
| 291. C4⋊C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291154 | 2 |
| #20290891 | 2 |
| #20290107 | 2 |
| #20290055 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284813 | 2 |
| #9323 | 53 |