Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
648 conjugacy classes of subgroups.
The subgroup lattice has 418 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×Q8⋊#88322 | C2 | semidirect |
| 4. #20272556 | C2 | semidirect |
| 69. C2×Q8×C53 | M16 | semidirect |
| 99. C4⋊C4×C53 | M16 | semidirect |
| 233. C53 | #8942 | semidirect |
| 278. C2×Q8 | #11719917 | semidirect |
| 315. C4⋊C4 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810647 | 2 |
| C4×C22⋊#88322 | 2 |
| C2×Q8⋊#88322 | 2 |
| #20272556 | 2 |
| C4×C22⋊Q8×C53 | 2 |
| #8942 | 53 |