Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. C2×#16811056 | C2 | semidirect |
| 2. #20277025 | C2 | direct (N × H) |
| 3. C2×#16810460 | C2 | semidirect |
| 4. C2×D1696 | C2 | semidirect |
| 5. C2×C32×D53 | C2 | semidirect |
| 6. C2×C53×Q64 | C2 | semidirect |
| 9. #16811056 | C22 | semidirect |
| 13. #16810460 | C22 | semidirect |
| 14. D1696 | C22 | semidirect |
| 16. C32×D53 | C22 | semidirect |
| 18. C53×Q64 | C22 | semidirect |
| 85. C2×Q64 | D53 | semidirect |
| 89. C2×C53 | #2262 | semidirect |
| 100. Q64 | C2×D53 | semidirect |
| 106. C53 | C2×#2262 | semidirect |
| 171. C2 | #20277025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811056 | 2 |
| #20277025 | 2 |
| C2×#16810460 | 2 |
| C2×D1696 | 2 |
| C2×C32×D53 | 2 |
| C2×C53×Q64 | 2 |
| C2×#2262 | 53 |