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 |
| 3. C2×#16810978 | C2 | direct (N × H) |
| 4. C22×#13133142 | C2 | semidirect |
| 6. C22×C4×C8×C53 | C2 | semidirect |
| 10. C2×#13133209 | C22 | semidirect |
| 16. #16810978 | C22 | direct (N × H) |
| 17. C2×#13133142 | C22 | semidirect |
| 21. C2×C4×C8×C53 | C22 | semidirect |
| 32. #13133209 | C23 | semidirect |
| 39. #13133142 | C23 | semidirect |
| 47. C4×C8×C53 | C23 | semidirect |
| 100. C22×C53 | #488 | semidirect |
| 117. C22×C4×C8 | D53 | semidirect |
| 118. C2×C53 | C2×#488 | semidirect |
| 136. C2×C4×C8 | C2×D53 | semidirect |
| 137. C53 | C22×#488 | semidirect |
| 163. C4×C8 | C22×D53 | semidirect |
| 218. C22 | #16810978 | direct (N × H) |
| 228. C2 | C2×#16810978 | 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 |
| C22×#13133205 | 2 |
| C2×#16810978 | 2 |
| C22×#13133142 | 2 |
| C22×#13133139 | 2 |
| C22×C4×C8×C53 | 2 |
| C22×#488 | 53 |