Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D31 |
| commutator | C22×C31 | C23×C4 |
| Fitting | C31×#383 | C2 |
| socle, cosocle | C23×C31 | C24 |
| prime radical | C22×D124 | C22 |
| hypercenter | #383 | D31 |
| hypocenter | C31 | #2337 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14520953 | C2 | semidirect |
| 3. #14520941 | C2 | semidirect |
| 4. #14520938 | C2 | semidirect |
| 6. #14520923 | C2 | semidirect |
| 7. C4×C4⋊Dic31 | C2 | semidirect |
| 8. #14520896 | C2 | semidirect |
| 9. C31×#383 | C2 | semidirect |
| 24. #11758452 | C4 | semidirect |
| 47. C2×Dic62 | C2×C4 | semidirect |
| 48. C42×C31 | C2×C4 | semidirect |
| 52. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 53. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 119. #383 | 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 |
| #14520941 | 2 |
| #14520938 | 2 |
| #14520927 | 2 |
| #14520923 | 2 |
| C4×C4⋊Dic31 | 2 |
| #14520896 | 2 |
| C31×#383 | 2 |
| #2337 | 31 |