Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20290858 | C2 | semidirect |
| 3. #20290230 | C2 | semidirect |
| 5. #20289623 | C2 | semidirect |
| 6. #20289599 | C2 | semidirect |
| 136. Q8×C53 | #101 | semidirect |
| 233. C53 | #9358 | semidirect |
| 340. Q8 | #13133278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291647 | 2 |
| #20290858 | 2 |
| #20290230 | 2 |
| #20290050 | 2 |
| #20289623 | 2 |
| #20289599 | 2 |
| #20284526 | 2 |
| #9358 | 53 |