Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
446 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624869 | C2 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624869 | C2 | semidirect |
| 2. C3⋊#4207 | C3 | semidirect |
| 4. #92297 | C3 | semidirect |
| 8. C3×#737 | C2×C3 | semidirect |
| 9. C33×C9 | D3 | semidirect |
| 14. #6891 | D3 | semidirect |
| 17. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 19. C3⋊(C3⋊D9) | C32 | semidirect |
| 50. C32×C9 | C2×C32 | semidirect |
| 106. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 139. C32 | #4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624869 | 2 |
| C3⋊#4207 | 3 |
| C32×C3⋊D9 | 3 |
| #92297 | 3 |
| #4169⋊C3 | 3 |
| #92258 | 3 |