Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20276939 | C2 | semidirect |
| 3. #20276863 | C2 | semidirect |
| 4. #20274114 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272677 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 10. #16811028 | C22 | semidirect |
| 20. #16810376 | C22 | semidirect |
| 23. C53×C4⋊C16 | C22 | semidirect |
| 24. C4×C16×C53 | C22 | semidirect |
| 150. D4⋊C16 | D53 | semidirect |
| 168. C4⋊C16 | C2×D53 | semidirect |
| 171. C4×C16 | C2×D53 | semidirect |
| 174. C53 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D424 | 2 |
| #20276939 | 2 |
| #20276863 | 2 |
| #20274114 | 2 |
| #20272762 | 2 |
| #20272677 | 2 |
| C53×D4⋊C16 | 2 |
| #12372 | 53 |