Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 121 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×C32×D53 | C2 | semidirect |
| 3. C22⋊#13133123 | C2 | semidirect |
| 4. #20272852 | C2 | semidirect |
| 5. C53×C22⋊C32 | C2 | semidirect |
| 13. C2×#13133123 | C22 | semidirect |
| 16. C2×C32×C53 | C22 | semidirect |
| 67. C22×D53 | C32 | semidirect |
| 91. C22×C53 | C2×C32 | semidirect |
| 98. C2×D53 | C2×C32 | semidirect |
| 109. C22⋊C32 | D53 | direct (N × H) |
| 115. D53 | C22⋊C32 | direct (N × H) |
| 126. C2×C32 | C2×D53 | semidirect |
| 127. C53 | C2×C22⋊C32 | semidirect |
| 208. C22 | C32×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D53 | 2 |
| C2×C32×D53 | 2 |
| C22⋊#13133123 | 2 |
| #20272852 | 2 |
| C53×C22⋊C32 | 2 |
| C2×C22⋊C32 | 53 |