Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 235 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×#13133162 | C2 | semidirect |
| 2. C22×D848 | C2 | semidirect |
| 3. C2×#16811007 | C2 | semidirect |
| 4. C2×#16811000 | C2 | semidirect |
| 5. #20276981 | C2 | direct (N × H) |
| 6. C2×C53×#346 | C2 | semidirect |
| 15. C2×#13133162 | C22 | semidirect |
| 17. C2×D848 | C22 | semidirect |
| 19. #16811007 | C22 | semidirect |
| 21. #16811000 | C22 | semidirect |
| 24. C53×#346 | C22 | semidirect |
| 53. C2×C16×C53 | D4 | semidirect |
| 93. C16×C53 | C2×D4 | semidirect |
| 142. C2×#346 | D53 | semidirect |
| 143. C2×C53 | #2250 | semidirect |
| 165. #346 | C2×D53 | semidirect |
| 166. C53 | C2×#2250 | semidirect |
| 195. C2×C16 | D212 | semidirect |
| 235. C16 | C2×D212 | semidirect |
| 280. C2 | #20276981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C22×D848 | 2 |
| C2×#16811007 | 2 |
| C2×#16811000 | 2 |
| #20276981 | 2 |
| C2×C53×#346 | 2 |
| C2×#2250 | 53 |