Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
356 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20290830 | C2 | semidirect |
| 4. #20289927 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289549 | C2 | semidirect |
| 23. #16810370 | C4 | semidirect |
| 24. #16810368 | C4 | semidirect |
| 25. #16810367 | C4 | semidirect |
| 26. C53×#331 | C4 | semidirect |
| 191. #331 | #6157 | semidirect |
| 196. C53 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290879 | 2 |
| #20290830 | 2 |
| #20290061 | 2 |
| #20289927 | 2 |
| #20289612 | 2 |
| #20289549 | 2 |
| #20273361 | 2 |
| #9592 | 53 |