Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C2×#16811513 | C2 | semidirect |
| 4. #20290522 | C2 | semidirect |
| 5. #20289786 | C2 | semidirect |
| 6. #20289780 | C2 | semidirect |
| 11. #16811664 | C4 | semidirect |
| 17. #16811541 | C4 | semidirect |
| 23. #16810425 | C4 | semidirect |
| 24. #16810424 | C4 | semidirect |
| 25. #16810423 | C4 | semidirect |
| 26. C53×#357 | C4 | semidirect |
| 36. #13133292 | C2×C4 | semidirect |
| 39. #13133287 | C2×C4 | semidirect |
| 58. C2×#11719908 | C2×C4 | semidirect |
| 59. #13133151 | C2×C4 | semidirect |
| 62. C2×C16×C53 | C2×C4 | semidirect |
| 63. #107×C53 | C2×C4 | semidirect |
| 198. #357 | #6157 | semidirect |
| 201. C53 | #12647 | semidirect |
| 226. C2×C16 | C2×#6157 | semidirect |
| 230. #107 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811664 | 2 |
| C2×#16811541 | 2 |
| C2×#16811513 | 2 |
| #20290522 | 2 |
| #20289786 | 2 |
| #20289780 | 2 |
| #20276429 | 2 |
| #12647 | 53 |