Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273339 | C2 | semidirect |
| 3. #20273222 | C2 | semidirect |
| 4. #20272608 | C2 | semidirect |
| 5. C53×#2372 | C2 | semidirect |
| 9. #16811018 | C4 | semidirect |
| 10. #16811013 | C4 | semidirect |
| 33. #13133217 | C2×C4 | semidirect |
| 34. #13133214 | C2×C4 | semidirect |
| 41. #13133128 | C2×C4 | semidirect |
| 166. #2372 | D53 | semidirect |
| 193. C53 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285179 | 2 |
| #20273339 | 2 |
| #20273222 | 2 |
| #20272608 | 2 |
| C53×#2372 | 2 |
| #9441 | 53 |