Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16810740 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20275579 | C2 | semidirect |
| 5. #20272823 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C53×#2139 | C2 | semidirect |
| 11. #16811058 | C4 | semidirect |
| 89. Q16×C53 | C22⋊C4 | semidirect |
| 93. D8×C53 | C22⋊C4 | semidirect |
| 182. #2139 | D53 | semidirect |
| 213. C53 | #13029 | semidirect |
| 275. Q16 | #11719921 | semidirect |
| 283. D8 | #11719921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C2×#16810740 | 2 |
| C2×#16810437 | 2 |
| #20275579 | 2 |
| #20272823 | 2 |
| #20272796 | 2 |
| C53×#2139 | 2 |
| #13029 | 53 |