Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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. #20290372 | C2 | semidirect |
| 4. #20289916 | C2 | semidirect |
| 5. #20289610 | C2 | semidirect |
| 6. #20289603 | C2 | semidirect |
| 8. #16811674 | C4 | semidirect |
| 9. Q8×#88324 | C4 | semidirect |
| 10. #16811657 | C4 | semidirect |
| 12. #16811651 | C4 | semidirect |
| 22. #16811480 | C4 | semidirect |
| 23. #16811479 | C4 | semidirect |
| 220. C53 | #8247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291531 | 2 |
| #20290372 | 2 |
| #20290168 | 2 |
| #20289916 | 2 |
| #20289610 | 2 |
| #20289603 | 2 |
| #20273200 | 2 |
| #8247 | 53 |