Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14521382 | C2 | semidirect |
| 3. #14521326 | C2 | semidirect |
| 4. #14521251 | C2 | semidirect |
| 6. #14521147 | C2 | semidirect |
| 7. #14521106 | C2 | semidirect |
| 8. C31×#533 | C2 | semidirect |
| 11. C31×C4⋊Q8 | C22 | semidirect |
| 12. C31×C4⋊Q8 | C22 | semidirect |
| 17. C4×Q8×C31 | C22 | semidirect |
| 27. #11758423 | C22 | semidirect |
| 30. #11758395 | C22 | semidirect |
| 31. C4⋊(C31⋊C8) | C22 | semidirect |
| 32. #11758391 | C22 | semidirect |
| 108. #533 | D31 | semidirect |
| 124. C4⋊Q8 | C2×D31 | semidirect |
| 125. C4⋊Q8 | C2×D31 | semidirect |
| 130. C4×Q8 | C2×D31 | semidirect |
| 145. C31 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| #14521382 | 2 |
| #14521326 | 2 |
| #14521251 | 2 |
| #14521199 | 2 |
| #14521147 | 2 |
| #14521106 | 2 |
| C31×#533 | 2 |
| #3110 | 31 |