Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 1. #20291647 | C2 | semidirect |
| 2. #20290857 | C2 | semidirect |
| 3. #20290222 | C2 | semidirect |
| 4. #20290050 | C2 | semidirect |
| 5. #20289623 | C2 | semidirect |
| 6. #20289599 | C2 | semidirect |
| 156. Q8×C53 | #100 | semidirect |
| 266. C53 | #9360 | semidirect |
| 390. Q8 | #13133277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291647 | 2 |
| #20290857 | 2 |
| #20290222 | 2 |
| #20290050 | 2 |
| #20289623 | 2 |
| #20289599 | 2 |
| #20284193 | 2 |
| #9360 | 53 |