Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 101 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. M64×D53 | C2 | semidirect |
| 3. #20272855 | C2 | semidirect |
| 4. #20272854 | C2 | semidirect |
| 5. C53×#1400 | C2 | semidirect |
| 14. #16810457 | C22 | semidirect |
| 18. C53×M64 | C22 | semidirect |
| 128. #1400 | D53 | direct (N × H) |
| 134. D53 | #1400 | direct (N × H) |
| 146. M64 | C2×D53 | semidirect |
| 148. C53 | C2×#1400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M32×D53 | 2 |
| M64×D53 | 2 |
| #20272855 | 2 |
| #20272854 | 2 |
| C53×#1400 | 2 |
| C2×#1400 | 53 |