Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#11758446 | C2 | semidirect |
| 4. #14521255 | C2 | direct (N × H) |
| 5. C2×#11758404 | C2 | semidirect |
| 6. C2×C31×C4⋊C8 | C2 | semidirect |
| 21. #11758446 | C22 | semidirect |
| 22. C31×C4⋊C8 | C22 | semidirect |
| 23. #11758404 | C22 | semidirect |
| 56. C2×C4×C31 | SD16 | semidirect |
| 86. C4×C31 | C2×SD16 | semidirect |
| 95. C2×C4⋊C8 | D31 | semidirect |
| 97. C2×C31 | #461 | semidirect |
| 117. C4⋊C8 | C2×D31 | semidirect |
| 119. C31 | C2×#461 | semidirect |
| 163. C2×C4 | #92470 | semidirect |
| 183. C4 | C2×#92470 | semidirect |
| 187. C2 | #14521255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C2×#11758446 | 2 |
| C2×C4×D124 | 2 |
| #14521255 | 2 |
| C2×#11758404 | 2 |
| C2×C31×C4⋊C8 | 2 |
| C2×#461 | 31 |