Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
178 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C31 |
| prime radical | C2×D8×C31 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ C4×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C31×Q32 | C2 | semidirect |
| 4. C31×#494 | C2 | semidirect |
| 5. C31×#346 | C2 | semidirect |
| 45. #2251 | C31 | direct (N × H) |
| 54. C2×Q32 | C2×C31 | semidirect |
| 57. #494 | C2×C31 | semidirect |
| 58. #346 | C2×C31 | semidirect |
| 73. C31 | #2251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×Q32 | 2 |
| C2×C31×SD32 | 2 |
| C31×#495 | 2 |
| C31×#494 | 2 |
| C31×#346 | 2 |
| #2251 | 31 |