Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20290944 | C2 | semidirect |
| 2. C2×#16811497 | C2 | semidirect |
| 3. #20289703 | C2 | semidirect |
| 4. #20289701 | C2 | semidirect |
| 14. #16810861 | C4 | semidirect |
| 16. #16810856 | C4 | semidirect |
| 20. #16810661 | C4 | semidirect |
| 22. C2×#135×C53 | C4 | semidirect |
| 46. #13133151 | C2×C4 | semidirect |
| 47. #13133151 | C2×C4 | semidirect |
| 55. C2×Q16×C53 | C2×C4 | semidirect |
| 57. C2×D8×C53 | C2×C4 | semidirect |
| 187. C2×#135 | #6157 | semidirect |
| 204. C53 | #11704 | semidirect |
| 209. C2×Q16 | C2×#6157 | semidirect |
| 211. C2×D8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290944 | 2 |
| C2×#16811497 | 2 |
| #20289703 | 2 |
| #20289701 | 2 |
| #20284292 | 2 |
| #11704 | 53 |