Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
516 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #10624565 |
| commutator, Frattini, cosocle | C32×C9 | C2×C33 |
| prime radical | C2×C3×H(3,𝔽3) | 3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C32×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14550737 | C2 | direct (N × H) |
| 3. C2×#10624709 | C3 | semidirect |
| 5. C2×#10624472 | C3 | semidirect |
| 6. C2×#10624471 | C3 | semidirect |
| 7. C2×#10624471 | C3 | semidirect |
| 8. C2×#10624471 | C3 | semidirect |
| 10. #10624709 | C2×C3 | semidirect |
| 12. #10624472 | C2×C3 | semidirect |
| 13. #10624471 | C2×C3 | semidirect |
| 14. #10624471 | C2×C3 | semidirect |
| 15. #10624471 | C2×C3 | semidirect |
| 65. C2×C27⋊C3 | 3−1+2 | semidirect |
| 103. C27⋊C3 | C2×3−1+2 | semidirect |
| 210. C2 | #14550737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14550737 | 2 |
| C2×#10624887 | 3 |
| C2×#10624709 | 3 |
| C2×#10624704 | 3 |
| C2×#10624472 | 3 |
| C2×#10624471 | 3 |