Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | C2×D4 |
| commutator | C2×C4 | C22×C4×C31 |
| Frattini, cosocle | C22×C4 | C23×C31 |
| socle | C22×C31 | C2×C22⋊C4 |
| prime radical | C31×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#423 | C2 | semidirect |
| 3. C2×C31×#104 | C2 | semidirect |
| 4. C43×C31 | C2 | semidirect |
| 7. C31×C4⋊Q8 | C4 | semidirect |
| 8. C31×#127 | C4 | semidirect |
| 9. C31×#124 | C4 | semidirect |
| 36. C42×C31 | D4 | semidirect |
| 56. #1962 | C31 | direct (N × H) |
| 65. C4×C31 | #104 | semidirect |
| 70. #423 | C2×C31 | semidirect |
| 71. C2×#104 | C2×C31 | semidirect |
| 72. C43 | C2×C31 | semidirect |
| 79. C4⋊Q8 | C4×C31 | semidirect |
| 80. #127 | C4×C31 | semidirect |
| 81. #124 | C4×C31 | semidirect |
| 89. C31 | #1962 | direct (N × H) |
| 109. C42 | D4×C31 | semidirect |
| 137. C4 | C31×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#532 | 2 |
| C31×#423 | 2 |
| C2×C31×#104 | 2 |
| C43×C31 | 2 |
| #1962 | 31 |