Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1050 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 259 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. #20277441 | C2 | semidirect |
| 2. #20275540 | C2 | semidirect |
| 3. #20275065 | C2 | semidirect |
| 4. #20274846 | C2 | semidirect |
| 5. #20274466 | C2 | semidirect |
| 18. C53×#493 | C4 | semidirect |
| 34. C2×D8×C53 | C2×C4 | semidirect |
| 37. #127×C53 | C2×C4 | semidirect |
| 39. C4×C8×C53 | C2×C4 | semidirect |
| 112. #493 | Dic53 | semidirect |
| 122. C53 | #22276 | semidirect |
| 127. C2×D8 | C2×Dic53 | semidirect |
| 131. #127 | C2×Dic53 | semidirect |
| 140. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277441 | 2 |
| #20275540 | 2 |
| #20275065 | 2 |
| #20274846 | 2 |
| #20274466 | 2 |
| C2×C53×#493 | 2 |
| #22276 | 53 |