Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20283633 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20275625 | C2 | semidirect |
| 6. #20272819 | C2 | semidirect |
| 7. C53×#1378 | C2 | semidirect |
| 13. C2×#13133162 | C4 | semidirect |
| 14. C2×D848 | C4 | semidirect |
| 171. #1378 | D53 | semidirect |
| 197. C53 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811061 | 2 |
| #20283633 | 2 |
| C2×#16810437 | 2 |
| #20276444 | 2 |
| #20275625 | 2 |
| #20272819 | 2 |
| C53×#1378 | 2 |
| #13036 | 53 |