Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1450 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 299 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. C2×#16811016 | C2 | semidirect |
| 2. C2×#16811002 | C2 | semidirect |
| 5. #20283111 | C2 | semidirect |
| 7. C4×#13133127 | C2 | semidirect |
| 8. C2×C53×#494 | C2 | semidirect |
| 51. #13133127 | D4 | semidirect |
| 141. C4×C53 | #497 | semidirect |
| 148. C2×#494 | D53 | semidirect |
| 179. C53 | #33305 | semidirect |
| 292. C4 | #16811016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811016 | 2 |
| C2×#16811002 | 2 |
| C2×#16810997 | 2 |
| C2×#16810996 | 2 |
| #20283111 | 2 |
| #20283073 | 2 |
| C4×#13133127 | 2 |
| C2×C53×#494 | 2 |
| #33305 | 53 |