Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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×#16810460 | C2 | semidirect |
| 3. #20272892 | C2 | semidirect |
| 4. C22⋊#13133123 | C2 | semidirect |
| 5. C53×#2216 | C2 | semidirect |
| 11. C2×#13133123 | C22 | semidirect |
| 12. C2×Q32×C53 | C22 | semidirect |
| 15. C53×#366 | C22 | semidirect |
| 78. C22×C53 | SD64 | semidirect |
| 91. #2216 | D53 | semidirect |
| 100. C2×Q32 | C2×D53 | semidirect |
| 108. #366 | C2×D53 | semidirect |
| 110. C53 | #13664 | semidirect |
| 175. C22 | #16810460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810460 | 2 |
| #20272892 | 2 |
| C22⋊#13133123 | 2 |
| C53×#2216 | 2 |
| #13664 | 53 |