Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2334 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1464 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×#13133291 | C2 | direct (N × H) |
| 2. C23×#11719910 | C2 | semidirect |
| 4. C2×#13133291 | C22 | direct (N × H) |
| 5. C22×#11719910 | C22 | semidirect |
| 11. #13133291 | C23 | direct (N × H) |
| 12. C2×#11719910 | C23 | semidirect |
| 36. #11719910 | C24 | semidirect |
| 38. C23×C53 | M32 | semidirect |
| 51. C22×C53 | C2×M32 | semidirect |
| 61. C2×C53 | C22×M32 | semidirect |
| 70. C53 | C23×M32 | semidirect |
| 98. C23 | #13133291 | direct (N × H) |
| 110. C22 | C2×#13133291 | direct (N × H) |
| 117. C2 | C22×#13133291 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133291 | 2 |
| C23×#11719910 | 2 |
| C24×#88322 | 2 |
| C23×M32 | 53 |