Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20290903 | C2 | semidirect |
| 4. #20290147 | C2 | semidirect |
| 5. #20289569 | C2 | semidirect |
| 6. #20289538 | C2 | semidirect |
| 22. #16810997 | C4 | semidirect |
| 23. #16810970 | C4 | semidirect |
| 24. #16810969 | C4 | semidirect |
| 28. C53×#492 | C4 | semidirect |
| 52. #13133217 | C2×C4 | semidirect |
| 68. C4×#88322 | C2×C4 | semidirect |
| 70. C4⋊Q8×C53 | C2×C4 | semidirect |
| 72. C4×C8×C53 | C2×C4 | semidirect |
| 110. C4×#6157 | SD16 | semidirect |
| 227. #492 | #6157 | semidirect |
| 244. C53 | #9295 | semidirect |
| 253. C4⋊Q8 | C2×#6157 | semidirect |
| 284. C4×C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291207 | 2 |
| #20290903 | 2 |
| #20290223 | 2 |
| #20290147 | 2 |
| #20289569 | 2 |
| #20289538 | 2 |
| #20285652 | 2 |
| #9295 | 53 |