Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D31 |
| commutator, socle | C22×C31 | C23×C4 |
| Fitting, prime radical | C31×#525 | C2 |
| cosocle | C2×C4×C31 | C24 |
| hypercenter | #525 | D31 |
| hypocenter | C31 | #2977 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14521121 | C2 | semidirect |
| 2. D4×C31⋊C8 | C2 | semidirect |
| 3. #14521110 | C2 | semidirect |
| 4. #14521016 | C2 | semidirect |
| 5. C2×C22⋊(C31⋊C8) | C2 | semidirect |
| 15. C2×#92474 | C22 | semidirect |
| 17. C22×C31⋊C8 | C22 | semidirect |
| 21. C22⋊(C31⋊C8) | C22 | semidirect |
| 22. C4⋊(C31⋊C8) | C22 | semidirect |
| 23. #11758391 | C22 | semidirect |
| 24. C4×C31⋊C8 | C22 | semidirect |
| 114. C31 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521121 | 2 |
| D4×C31⋊C8 | 2 |
| #14521110 | 2 |
| #14521016 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C31×#525 | 2 |
| #2977 | 31 |