Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
684 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #20273288 | C2 | semidirect |
| 4. #20272583 | C2 | semidirect |
| 8. #16810559 | C4 | semidirect |
| 10. #16810535 | C4 | semidirect |
| 21. C22×Dic106 | C2×C4 | semidirect |
| 28. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 41. #13133124 | C2×C4 | semidirect |
| 213. C53 | #9199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280520 | 2 |
| #20277329 | 2 |
| #20273288 | 2 |
| #20272583 | 2 |
| C2×C53×#323 | 2 |
| #9199 | 53 |