Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C22×#92474 | C2 | semidirect |
| 3. #14521053 | C2 | direct (N × H) |
| 4. C2×#11758397 | C2 | semidirect |
| 5. C2×C31×#117 | C2 | semidirect |
| 11. C22×D124 | C4 | semidirect |
| 15. C31×#117 | C22 | semidirect |
| 16. C2×C4⋊C4×C31 | C22 | semidirect |
| 20. C2×#92474 | C22 | semidirect |
| 21. C22×C31⋊C8 | C22 | semidirect |
| 22. #11758397 | C22 | semidirect |
| 42. C2×D124 | C2×C4 | semidirect |
| 45. C4⋊C4×C31 | C23 | semidirect |
| 50. C2×C31⋊C8 | C23 | semidirect |
| 95. C2×#117 | D31 | semidirect |
| 99. C2×C31 | #418 | semidirect |
| 115. #117 | C2×D31 | semidirect |
| 116. C2×C4⋊C4 | C2×D31 | semidirect |
| 120. C31 | C2×#418 | semidirect |
| 146. C4⋊C4 | C22×D31 | semidirect |
| 192. C2 | #14521053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D124 | 2 |
| C22×#92474 | 2 |
| #14521053 | 2 |
| C2×#11758397 | 2 |
| C2×C31×#117 | 2 |
| C2×#418 | 31 |