Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 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. #14521326 | C2 | direct (N × H) |
| 3. C2×#11758395 | C2 | semidirect |
| 4. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 6. C2×C31×C4⋊Q8 | C2 | semidirect |
| 11. C31×C4⋊Q8 | C22 | semidirect |
| 21. #11758395 | C22 | semidirect |
| 22. C4⋊(C31⋊C8) | C22 | semidirect |
| 33. C2×D124 | Q8 | semidirect |
| 67. D124 | C2×Q8 | semidirect |
| 86. C2×C4⋊Q8 | D31 | semidirect |
| 92. C2×C31 | #474 | semidirect |
| 102. C4⋊Q8 | C2×D31 | semidirect |
| 113. C31 | C2×#474 | semidirect |
| 177. C2 | #14521326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| #14521326 | 2 |
| C2×#11758395 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×#11758397 | 2 |
| C2×C31×C4⋊Q8 | 2 |
| C2×#474 | 31 |