Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 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. #14520953 | C2 | semidirect |
| 3. #14520940 | C2 | semidirect |
| 4. #14520939 | C2 | semidirect |
| 6. #14520920 | C2 | semidirect |
| 7. #14520917 | C2 | semidirect |
| 8. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 9. C4×C4⋊C4×C31 | C2 | semidirect |
| 24. #11758452 | C4 | semidirect |
| 47. C2×Dic62 | C2×C4 | semidirect |
| 51. C42×C31 | C2×C4 | semidirect |
| 55. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 56. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 120. C4×C4⋊C4 | D31 | semidirect |
| 150. C31 | #2337 | semidirect |
| 177. C42 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758452 | 2 |
| #14520953 | 2 |
| #14520940 | 2 |
| #14520939 | 2 |
| #14520927 | 2 |
| #14520920 | 2 |
| #14520917 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| C4×C4⋊C4×C31 | 2 |
| #2337 | 31 |