Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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×#16810462 | C2 | semidirect |
| 3. C2×#16810461 | C2 | semidirect |
| 4. #20276807 | C2 | semidirect |
| 5. #20272892 | C2 | semidirect |
| 6. #20272852 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 9. C2×Dic424 | C22 | semidirect |
| 18. C2×#13133123 | C22 | semidirect |
| 21. C2×C32×C53 | C22 | semidirect |
| 22. C53×#366 | C22 | semidirect |
| 105. C2×D53 | SD64 | semidirect |
| 116. #1415 | D53 | semidirect |
| 136. C2×C32 | C2×D53 | semidirect |
| 137. #366 | C2×D53 | semidirect |
| 139. C53 | #13664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| C2×#16810462 | 2 |
| C2×#16810461 | 2 |
| #20276807 | 2 |
| #20272892 | 2 |
| #20272852 | 2 |
| C53×#1415 | 2 |
| #13664 | 53 |