Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283303 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. C2×#16810404 | C2 | semidirect |
| 5. #20272817 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 12. #16810878 | C4 | semidirect |
| 13. #16810873 | C4 | semidirect |
| 54. #13133149 | C2×C4 | semidirect |
| 55. #13133149 | D4 | semidirect |
| 64. C2×Q16×C53 | C2×C4 | semidirect |
| 66. C2×D8×C53 | C2×C4 | semidirect |
| 73. #106×C53 | D4 | semidirect |
| 190. #2145 | D53 | semidirect |
| 219. C53 | #13008 | semidirect |
| 226. C2×Q16 | C4×D53 | semidirect |
| 228. C2×D8 | C4×D53 | semidirect |
| 264. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284320 | 2 |
| #20283303 | 2 |
| #20276451 | 2 |
| C2×#16810404 | 2 |
| #20272817 | 2 |
| #20272816 | 2 |
| C53×#2145 | 2 |
| #13008 | 53 |