Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
852 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 248 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×#121 | 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 |
|---|---|---|
| 1. C23×Q8×C31 | C2 | semidirect |
| 2. C2×C31×#124 | C2 | semidirect |
| 4. C31×#393 | C2 | semidirect |
| 5. C31×#391 | C2 | semidirect |
| 6. C31×#386 | C2 | semidirect |
| 7. C4×C22⋊C4×C31 | C2 | semidirect |
| 32. C2×Q8×C31 | D4 | semidirect |
| 78. #2436 | C31 | direct (N × H) |
| 86. C22×C31 | #124 | semidirect |
| 96. C23×Q8 | C2×C31 | semidirect |
| 97. C2×#124 | C2×C31 | semidirect |
| 99. #393 | C2×C31 | semidirect |
| 100. #391 | C2×C31 | semidirect |
| 101. #386 | C2×C31 | semidirect |
| 102. C4×C22⋊C4 | C2×C31 | semidirect |
| 126. C31 | #2436 | direct (N × H) |
| 134. C2×Q8 | D4×C31 | semidirect |
| 187. C22 | C31×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C31 | 2 |
| C2×C31×#124 | 2 |
| C2×C31×#121 | 2 |
| C31×#393 | 2 |
| C31×#391 | 2 |
| C31×#386 | 2 |
| C4×C22⋊C4×C31 | 2 |
| #2436 | 31 |