Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1068 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 288 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 | C25×C31 | C22 |
| 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. C2×C31×C22⋊Q8 | C2 | semidirect |
| 3. C31×#385 | C2 | semidirect |
| 4. C31×#380 | C2 | semidirect |
| 7. C22×Q8×C31 | C22 | semidirect |
| 12. C2×C4⋊C4×C31 | C22 | semidirect |
| 13. C2×C4⋊C4×C31 | C22 | semidirect |
| 16. C31×#95 | C22 | semidirect |
| 19. C24×C31 | Q8 | semidirect |
| 53. #2848 | C31 | direct (N × H) |
| 59. C22×C31 | C22⋊Q8 | semidirect |
| 68. C2×C22⋊Q8 | C2×C31 | semidirect |
| 69. #385 | C2×C31 | semidirect |
| 70. #380 | C2×C31 | semidirect |
| 77. C22×Q8 | C22×C31 | semidirect |
| 82. C2×C4⋊C4 | C22×C31 | semidirect |
| 83. C2×C4⋊C4 | C22×C31 | semidirect |
| 86. #95 | C22×C31 | semidirect |
| 87. C31 | #2848 | direct (N × H) |
| 90. C24 | Q8×C31 | semidirect |
| 129. C22 | C31×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C31 | 2 |
| C2×C31×C22⋊Q8 | 2 |
| C31×#385 | 2 |
| C31×#380 | 2 |
| C31×#379 | 2 |
| #2848 | 31 |