Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2046 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 347 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×#16811000 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. C2×#16810998 | C2 | semidirect |
| 4. #20283109 | C2 | semidirect |
| 5. C4×C8×Dic53 | C2 | semidirect |
| 6. C2×C53×#493 | C2 | semidirect |
| 36. C4×#88322 | D4 | semidirect |
| 37. C8×Dic53 | D4 | semidirect |
| 46. C4×C8×C53 | D4 | semidirect |
| 70. C4×Dic53 | D8 | semidirect |
| 96. C8×C53 | #127 | semidirect |
| 97. #88322 | #127 | semidirect |
| 108. C4×C53 | #493 | semidirect |
| 111. Dic53 | #493 | semidirect |
| 115. C2×#493 | D53 | semidirect |
| 138. C53 | #33301 | semidirect |
| 163. C4×C8 | C22⋊D53 | semidirect |
| 214. C8 | #13133213 | semidirect |
| 225. C4 | #16810998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810999 | 2 |
| C2×#16810998 | 2 |
| #20283109 | 2 |
| C4×C8×Dic53 | 2 |
| C2×C53×#493 | 2 |
| #33301 | 53 |