Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
272 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 92 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×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C31 |
| Frattini, cosocle | C22×C4 | C23×C31 |
| prime radical | C31×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#432 | C2 | semidirect |
| 3. C31×#376 | C2 | semidirect |
| 4. C31×#327 | C2 | semidirect |
| 6. C31×C4⋊Q8 | C4 | semidirect |
| 7. C31×#127 | C4 | semidirect |
| 12. C4×D4×C31 | C4 | semidirect |
| 63. #1505 | C31 | direct (N × H) |
| 80. #432 | C2×C31 | semidirect |
| 81. #376 | C2×C31 | semidirect |
| 82. #327 | C2×C31 | semidirect |
| 89. C4⋊Q8 | C4×C31 | semidirect |
| 90. #127 | C4×C31 | semidirect |
| 95. C4×D4 | C4×C31 | semidirect |
| 103. C31 | #1505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#532 | 2 |
| C31×#432 | 2 |
| C31×#376 | 2 |
| C31×#327 | 2 |
| #1505 | 31 |