Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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×#13133211 | C2 | semidirect |
| 2. #20282789 | C2 | direct (N × H) |
| 3. C2×#16810553 | C2 | semidirect |
| 4. C2×#16810545 | C2 | semidirect |
| 6. C2×C53×#384 | C2 | semidirect |
| 9. C2×#13133211 | C22 | semidirect |
| 14. #16810553 | C22 | semidirect |
| 15. #16810545 | C22 | semidirect |
| 22. C53×#384 | C22 | semidirect |
| 45. C2×C42×C53 | D4 | semidirect |
| 69. C42×C53 | C2×D4 | semidirect |
| 118. C2×#384 | D53 | semidirect |
| 119. C2×C53 | #2823 | semidirect |
| 137. #384 | C2×D53 | semidirect |
| 140. C53 | C2×#2823 | semidirect |
| 161. C2×C42 | D212 | semidirect |
| 191. C42 | C2×D212 | semidirect |
| 231. C2 | #20282789 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133211 | 2 |
| #20282789 | 2 |
| C2×#16810553 | 2 |
| C2×#16810545 | 2 |
| C2×#16810540 | 2 |
| C2×C53×#384 | 2 |
| C2×#2823 | 53 |