Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
612 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275658 | C2 | semidirect |
| 3. #20273226 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 10. #16810903 | C4 | semidirect |
| 11. #16810828 | C4 | semidirect |
| 31. #13133217 | C2×C4 | semidirect |
| 32. #13133217 | C2×C4 | semidirect |
| 41. C4⋊#88322 | C2×C4 | semidirect |
| 214. C53 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284814 | 2 |
| #20275658 | 2 |
| #20273226 | 2 |
| #20273158 | 2 |
| #20272608 | 2 |
| #20272571 | 2 |
| C53×#2275 | 2 |
| #9323 | 53 |