Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×#92481 | C2 | semidirect |
| 3. #14521199 | C2 | direct (N × H) |
| 4. C2×#11758397 | C2 | semidirect |
| 5. C2×C22⋊(C31⋊C8) | C2 | semidirect |
| 6. C2×C31×C22⋊Q8 | C2 | semidirect |
| 8. C22×Q8×C31 | C22 | semidirect |
| 16. C31×C22⋊Q8 | C22 | semidirect |
| 18. C2×C4⋊C4×C31 | C22 | semidirect |
| 21. C2×#92481 | C22 | semidirect |
| 22. C22×C31⋊C8 | C22 | semidirect |
| 23. C22⋊(C31⋊C8) | C22 | semidirect |
| 24. #11758397 | C22 | semidirect |
| 33. C2×Q8×C31 | C23 | semidirect |
| 51. C4⋊C4×C31 | C23 | semidirect |
| 55. C2×C31⋊C8 | C23 | semidirect |
| 58. C23×C31 | SD16 | semidirect |
| 93. C22×C31 | C2×SD16 | semidirect |
| 108. C2×C22⋊Q8 | D31 | semidirect |
| 113. C2×C31 | #450 | semidirect |
| 119. C22×Q8 | C2×D31 | semidirect |
| 130. C22⋊Q8 | C2×D31 | semidirect |
| 132. C2×C4⋊C4 | C2×D31 | semidirect |
| 136. C31 | C2×#450 | semidirect |
| 145. C2×Q8 | C22×D31 | semidirect |
| 166. C4⋊C4 | C22×D31 | semidirect |
| 178. C23 | #92481 | semidirect |
| 209. C22 | C2×#92481 | semidirect |
| 219. C2 | #14521199 | 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×#92481 | 2 |
| #14521199 | 2 |
| C2×#11758397 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C2×C31×C22⋊Q8 | 2 |
| C2×#450 | 31 |