Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16810457 | C2 | semidirect |
| 3. #20272898 | C2 | semidirect |
| 4. C2×C53×#368 | C2 | semidirect |
| 15. C2×#13133123 | C22 | semidirect |
| 19. C53×#368 | C22 | semidirect |
| 109. C2×#368 | D53 | semidirect |
| 130. #368 | C2×D53 | semidirect |
| 131. C53 | #13620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| C2×#16810457 | 2 |
| #20272898 | 2 |
| C2×C53×#368 | 2 |
| #13620 | 53 |