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 |
|---|---|---|
| 3. #20276435 | C2 | semidirect |
| 5. #20272821 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 13. #16810878 | C4 | semidirect |
| 53. #13133149 | C2×C4 | semidirect |
| 62. C2×Q16×C53 | C2×C4 | semidirect |
| 176. #2141 | D53 | semidirect |
| 203. C53 | #13000 | semidirect |
| 211. C2×Q16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810878 | 2 |
| #20283303 | 2 |
| #20276435 | 2 |
| C2×#16810404 | 2 |
| #20272821 | 2 |
| #20272820 | 2 |
| C53×#2141 | 2 |
| #13000 | 53 |