Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20290654 | C2 | semidirect |
| 3. #20290292 | C2 | semidirect |
| 5. #20289601 | C2 | semidirect |
| 6. #20289547 | C2 | semidirect |
| 110. Q8×C53 | #108 | semidirect |
| 196. C53 | #8899 | semidirect |
| 278. Q8 | #13133287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291649 | 2 |
| #20290654 | 2 |
| #20290292 | 2 |
| #20290053 | 2 |
| #20289601 | 2 |
| #20289547 | 2 |
| #20273096 | 2 |
| #8899 | 53 |