Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C31 | C22×C42 |
| Fitting | C31×#376 | C2 |
| socle, cosocle | C23×C31 | C24 |
| prime radical | C22×D124 | C22 |
| hypercenter | #376 | D31 |
| hypocenter | C31 | #2275 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C4⋊Dic31 | C2 | semidirect |
| 3. #14520896 | C2 | semidirect |
| 4. #95×D31 | C2 | semidirect |
| 5. C31×#376 | C2 | semidirect |
| 12. C4×D124 | C4 | semidirect |
| 23. C2×C4×D31 | C2×C4 | semidirect |
| 24. C42×C31 | C2×C4 | semidirect |
| 25. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 26. C4⋊Dic31 | C2×C4 | semidirect |
| 40. D124 | C42 | semidirect |
| 56. #376 | D31 | semidirect |
| 72. C31 | #2275 | semidirect |
| 84. C42 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| C4×C4⋊Dic31 | 2 |
| #14520896 | 2 |
| #95×D31 | 2 |
| C31×#376 | 2 |
| #2275 | 31 |