Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D31 |
| commutator, socle, cosocle | C22×C31 | C25 |
| Fitting | C2×C31×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D31 |
| hypocenter | C31 | #3486 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D31 | C2 | semidirect |
| 2. Q8×C22⋊D31 | C2 | semidirect |
| 3. #14521706 | C2 | semidirect |
| 4. #14521620 | C2 | semidirect |
| 5. #14521556 | C2 | semidirect |
| 6. #14521527 | C2 | semidirect |
| 7. C2×C31×2−1+4 | C2 | semidirect |
| 10. C2×#41×C31 | C22 | semidirect |
| 12. C22×Q8×C31 | C22 | semidirect |
| 18. Q8×Dic31 | C22 | semidirect |
| 19. #11758521 | C22 | semidirect |
| 22. #11758513 | C22 | semidirect |
| 26. #11758501 | C22 | semidirect |
| 31. C2×Q8×C31 | D4 | semidirect |
| 79. C2×D31 | 2−1+4 | semidirect |
| 84. C2×2−1+4 | D31 | semidirect |
| 98. C2×#41 | C2×D31 | semidirect |
| 103. C22×Q8 | C2×D31 | semidirect |
| 115. C31 | #3486 | semidirect |
| 123. C2×Q8 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D31 | 2 |
| Q8×C22⋊D31 | 2 |
| #14521706 | 2 |
| #14521620 | 2 |
| #14521556 | 2 |
| #14521527 | 2 |
| C2×C31×2−1+4 | 2 |
| #3486 | 31 |