Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #20277762 | C2 | semidirect |
| 3. #20275550 | C2 | semidirect |
| 4. #20273282 | C2 | semidirect |
| 5. C2×#16810356 | C2 | semidirect |
| 6. #20272561 | C2 | semidirect |
| 7. C53×#1294 | C2 | semidirect |
| 12. #16810937 | C4 | semidirect |
| 15. #16810759 | C4 | semidirect |
| 31. C22×D212 | C2×C4 | semidirect |
| 48. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 76. C22⋊C8×C53 | C2×C4 | semidirect |
| 131. C22⋊Dic53 | D8 | semidirect |
| 264. #1294 | D53 | semidirect |
| 300. C53 | #9277 | semidirect |
| 343. C22⋊C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285466 | 2 |
| #20277762 | 2 |
| #20275550 | 2 |
| #20273282 | 2 |
| C2×#16810356 | 2 |
| #20272561 | 2 |
| C53×#1294 | 2 |
| #9277 | 53 |