Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20277033 | C2 | direct (N × H) |
| 3. C2×#16810463 | C2 | semidirect |
| 4. C2×#16810460 | C2 | semidirect |
| 5. C2×#16810457 | C2 | semidirect |
| 6. C22×Q32×C53 | C2 | semidirect |
| 13. #16810463 | C22 | semidirect |
| 14. #16810460 | C22 | semidirect |
| 15. #16810457 | C22 | semidirect |
| 21. C2×Q32×C53 | C22 | semidirect |
| 108. C22×Q32 | D53 | semidirect |
| 114. C2×C53 | #2264 | semidirect |
| 125. C2×Q32 | C2×D53 | semidirect |
| 133. C53 | C2×#2264 | semidirect |
| 219. C2 | #20277033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| #20277033 | 2 |
| C2×#16810463 | 2 |
| C2×#16810460 | 2 |
| C2×#16810457 | 2 |
| C22×Q32×C53 | 2 |
| C2×#2264 | 53 |