Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1450 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 363 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×#16811017 | C2 | semidirect |
| 2. C2×#16811003 | C2 | semidirect |
| 4. #20283113 | C2 | semidirect |
| 6. C4×#97×C53 | C2 | semidirect |
| 44. #97×C53 | D4 | semidirect |
| 100. C4×C53 | #497 | semidirect |
| 109. C4×#97 | D53 | semidirect |
| 129. C53 | #33305 | semidirect |
| 152. #97 | D212 | semidirect |
| 209. C4 | #16811017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811017 | 2 |
| C2×#16811003 | 2 |
| C2×#16810996 | 2 |
| #20283113 | 2 |
| #20283072 | 2 |
| C4×#97×C53 | 2 |
| #33305 | 53 |