Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 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. #20283568 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276430 | C2 | semidirect |
| 5. #20272816 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#1976 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 13. C2×#13133158 | C4 | semidirect |
| 45. C2×#11719908 | C2×C4 | semidirect |
| 54. C2×Q16×C53 | C2×C4 | semidirect |
| 56. C2×D8×C53 | C2×C4 | semidirect |
| 172. #1976 | D53 | semidirect |
| 200. C53 | #13033 | semidirect |
| 207. C2×Q16 | C4×D53 | semidirect |
| 215. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| #20283568 | 2 |
| #20276451 | 2 |
| #20276430 | 2 |
| #20272816 | 2 |
| #20272801 | 2 |
| C53×#1976 | 2 |
| #13033 | 53 |