Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
| 109. #1400 | D53 | semidirect |
| 128. C53 | #13556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811041 | 2 |
| M64×D53 | 2 |
| #20272855 | 2 |
| #20272854 | 2 |
| C53×#1400 | 2 |
| #13556 | 53 |