Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#533 | C2 | semidirect |
| 3. C31×#489 | C2 | semidirect |
| 4. C31×#488 | C2 | semidirect |
| 5. C31×#419 | C2 | semidirect |
| 7. C4×M16×C31 | C2 | semidirect |
| 11. C31×C4⋊Q8 | C22 | semidirect |
| 12. C31×#125 | C22 | semidirect |
| 21. C31×#103 | C22 | semidirect |
| 23. C31×#97 | C22 | semidirect |
| 24. C4×C8×C31 | C22 | semidirect |
| 67. #3140 | C31 | direct (N × H) |
| 80. #533 | C2×C31 | semidirect |
| 82. #489 | C2×C31 | semidirect |
| 83. #488 | C2×C31 | semidirect |
| 84. #419 | C2×C31 | semidirect |
| 86. C4×M16 | C2×C31 | semidirect |
| 94. C4⋊Q8 | C22×C31 | semidirect |
| 95. #125 | C22×C31 | semidirect |
| 104. #103 | C22×C31 | semidirect |
| 106. #97 | C22×C31 | semidirect |
| 107. C4×C8 | C22×C31 | semidirect |
| 108. C31 | #3140 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#533 | 2 |
| C2×C31×#124 | 2 |
| C31×#489 | 2 |
| C31×#488 | 2 |
| C31×#419 | 2 |
| C31×#418 | 2 |
| C4×M16×C31 | 2 |
| #3140 | 31 |