Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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. C2×#16810705 | C2 | semidirect |
| 3. #20276590 | C2 | direct (N × H) |
| 4. C2×#16810423 | C2 | semidirect |
| 5. C2×#16810398 | C2 | semidirect |
| 6. C2×C53×#367 | C2 | semidirect |
| 9. C2×D848 | C4 | semidirect |
| 13. #16810705 | C22 | semidirect |
| 16. #16810423 | C22 | semidirect |
| 17. #16810398 | C22 | semidirect |
| 20. C53×#367 | C22 | semidirect |
| 25. C2×D424 | C2×C4 | semidirect |
| 32. D848 | C2×C4 | semidirect |
| 40. C2×C16×C53 | C2×C4 | semidirect |
| 67. D424 | C22×C4 | semidirect |
| 68. C16×C53 | C22×C4 | semidirect |
| 107. C2×#367 | D53 | semidirect |
| 110. C2×C53 | #2177 | semidirect |
| 125. #367 | C2×D53 | semidirect |
| 128. C53 | C2×#2177 | semidirect |
| 145. C2×C16 | C4×D53 | semidirect |
| 177. C16 | C2×C4×D53 | semidirect |
| 212. C2 | #20276590 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810705 | 2 |
| #20276590 | 2 |
| C2×#16810423 | 2 |
| C2×#16810398 | 2 |
| C2×C53×#367 | 2 |
| C2×#2177 | 53 |