Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 126 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. #20290442 | C2 | semidirect |
| 3. #20289891 | C2 | semidirect |
| 4. #20289588 | C2 | semidirect |
| 12. #16811474 | C4 | semidirect |
| 16. #16810526 | C4 | semidirect |
| 17. #16810519 | C4 | semidirect |
| 21. C4×C4⋊Dic53 | C4 | semidirect |
| 23. C2×C4×D4×C53 | C4 | semidirect |
| 27. #13133274 | C2×C4 | semidirect |
| 32. (C2×#6157)⋊C4 | C2×C4 | semidirect |
| 234. C2×C4×D4 | #6157 | semidirect |
| 250. C53 | #8216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290442 | 2 |
| C2×#16811474 | 2 |
| #20289891 | 2 |
| #20289588 | 2 |
| C4×#13133188 | 2 |
| #8216 | 53 |