Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1762 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1762 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×#16811012 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810996 | C2 | semidirect |
| 4. #20283110 | C2 | semidirect |
| 5. #20283072 | C2 | semidirect |
| 6. C4×#97×C53 | C2 | semidirect |
| 45. #97×C53 | D4 | semidirect |
| 46. C4×C8×C53 | D4 | semidirect |
| 97. C8×C53 | #127 | semidirect |
| 109. C4×C53 | #496 | semidirect |
| 117. C4×#97 | D53 | semidirect |
| 138. C53 | #33304 | semidirect |
| 162. #97 | D212 | semidirect |
| 163. C4×C8 | D212 | semidirect |
| 214. C8 | #13133214 | semidirect |
| 226. C4 | #16811012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811012 | 2 |
| C2×#16811000 | 2 |
| C2×#16810996 | 2 |
| #20283110 | 2 |
| #20283072 | 2 |
| C4×#97×C53 | 2 |
| #33304 | 53 |