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. #20283600 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. C2×#16810434 | C2 | semidirect |
| 5. #20275613 | C2 | semidirect |
| 6. #20272821 | C2 | semidirect |
| 7. C53×#1378 | C2 | semidirect |
| 12. #16811066 | C4 | semidirect |
| 14. #16811061 | C4 | semidirect |
| 39. C2×Dic212 | C2×C4 | semidirect |
| 43. C2×D424 | C2×C4 | semidirect |
| 70. M32×C53 | C2×C4 | semidirect |
| 190. #1378 | D53 | semidirect |
| 218. C53 | #13030 | semidirect |
| 252. M32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20283600 | 2 |
| #20276452 | 2 |
| C2×#16810434 | 2 |
| #20275613 | 2 |
| #20272821 | 2 |
| C53×#1378 | 2 |
| #13030 | 53 |