Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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×#13133209 | C2 | semidirect |
| 2. C2×#16810977 | C2 | direct (N × H) |
| 3. C22×#13133141 | C2 | semidirect |
| 5. C22×C4×#88322 | C2 | semidirect |
| 9. C2×#13133209 | C22 | semidirect |
| 12. #16810977 | C22 | direct (N × H) |
| 13. C2×#13133141 | C22 | semidirect |
| 15. C2×C4×#88322 | C22 | semidirect |
| 26. #13133209 | C23 | semidirect |
| 30. #13133141 | C23 | semidirect |
| 32. C4×#88322 | C23 | semidirect |
| 103. C22×C53 | #488 | semidirect |
| 119. C2×C53 | C2×#488 | semidirect |
| 137. C53 | C22×#488 | semidirect |
| 218. C22 | #16810977 | direct (N × H) |
| 228. C2 | C2×#16810977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133209 | 2 |
| C2×#16810977 | 2 |
| C22×#13133141 | 2 |
| C22×#13133138 | 2 |
| C22×C4×#88322 | 2 |
| C22×#124×C53 | 2 |
| C22×#488 | 53 |