Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 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. C4×#13133271 | C2 | semidirect |
| 4. #20289927 | C2 | semidirect |
| 5. #20289547 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 8. #16811672 | C4 | semidirect |
| 10. D4×#88324 | C4 | semidirect |
| 25. #16810355 | C4 | semidirect |
| 26. #16810353 | C4 | semidirect |
| 27. D4⋊#88322 | C4 | semidirect |
| 28. C53×D4⋊C8 | C4 | semidirect |
| 117. D4×C53 | #97 | semidirect |
| 138. Dic106 | #97 | semidirect |
| 142. #88324 | #104 | semidirect |
| 197. D4⋊C8 | #6157 | semidirect |
| 200. C53 | #8192 | semidirect |
| 289. D4 | #13133271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291520 | 2 |
| C4×#13133281 | 2 |
| C4×#13133271 | 2 |
| #20289927 | 2 |
| #20289547 | 2 |
| #20289542 | 2 |
| #20273094 | 2 |
| #8192 | 53 |