Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
702 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C2×C31×#120 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C4×C31 | C2 | semidirect |
| 3. C31×#397 | C2 | semidirect |
| 4. C31×#394 | C2 | semidirect |
| 5. C31×#386 | C2 | semidirect |
| 6. C31×#385 | C2 | semidirect |
| 7. C31×#379 | C2 | semidirect |
| 13. C2×C4⋊C4×C31 | C22 | semidirect |
| 20. C2×C22⋊C4×C31 | C22 | semidirect |
| 21. C31×#95 | C22 | semidirect |
| 22. C31×#95 | C22 | semidirect |
| 73. #2622 | C31 | direct (N × H) |
| 93. C22×C22⋊C4 | C2×C31 | semidirect |
| 94. #397 | C2×C31 | semidirect |
| 95. #394 | C2×C31 | semidirect |
| 96. #386 | C2×C31 | semidirect |
| 97. #385 | C2×C31 | semidirect |
| 98. #379 | C2×C31 | semidirect |
| 110. C2×C4⋊C4 | C22×C31 | semidirect |
| 117. C2×C22⋊C4 | C22×C31 | semidirect |
| 118. #95 | C22×C31 | semidirect |
| 119. #95 | C22×C31 | semidirect |
| 120. C31 | #2622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#120 | 2 |
| C22×C22⋊C4×C31 | 2 |
| C31×#397 | 2 |
| C31×#394 | 2 |
| C31×#386 | 2 |
| C31×#385 | 2 |
| C31×#379 | 2 |
| #2622 | 31 |