Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×D848 | C2 | semidirect |
| 2. C22×#13133156 | C2 | semidirect |
| 3. C2×#16810860 | C2 | semidirect |
| 4. #20276819 | C2 | direct (N × H) |
| 5. C2×#16810423 | C2 | semidirect |
| 6. C2×C53×#367 | C2 | semidirect |
| 11. C2×D848 | C22 | semidirect |
| 13. C2×#13133156 | C22 | semidirect |
| 16. #16810860 | C22 | semidirect |
| 18. #16810423 | C22 | semidirect |
| 21. C53×#367 | C22 | semidirect |
| 44. C2×C16×C53 | D4 | semidirect |
| 78. C16×C53 | C2×D4 | semidirect |
| 127. C2×#367 | D53 | semidirect |
| 129. C2×C53 | #2218 | semidirect |
| 147. #367 | C2×D53 | semidirect |
| 149. C53 | C2×#2218 | semidirect |
| 171. C2×C16 | D212 | semidirect |
| 207. C16 | C2×D212 | semidirect |
| 252. C2 | #20276819 | 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 |
| C22×#13133156 | 2 |
| C2×#16810860 | 2 |
| #20276819 | 2 |
| C2×#16810423 | 2 |
| C2×C53×#367 | 2 |
| C2×#2218 | 53 |