Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
406 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C31×C4⋊Q8 | C2 | semidirect |
| 3. C2×C31×#103 | C2 | semidirect |
| 5. C31×#336 | C2 | semidirect |
| 60. C2×C4×C31 | SD16 | semidirect |
| 66. #2013 | C31 | direct (N × H) |
| 83. C2×C4⋊Q8 | C2×C31 | semidirect |
| 84. C2×#103 | C2×C31 | semidirect |
| 86. #336 | C2×C31 | semidirect |
| 105. C31 | #2013 | direct (N × H) |
| 148. C2×C4 | SD16×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C31 | 2 |
| C2×C31×C4⋊Q8 | 2 |
| C2×C31×#103 | 2 |
| C31×#390 | 2 |
| C31×#336 | 2 |
| #2013 | 31 |