Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
467 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 467 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C3×C92 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C9×#737 | C2 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#737 | C2 | semidirect |
| 3. C3⋊(C9⋊D9) | C3 | semidirect |
| 11. C9×3−1+2 | D3 | semidirect |
| 15. #6887 | D3 | semidirect |
| 17. C3×C92 | D3 | semidirect |
| 18. C3×C92 | C2×C3 | semidirect |
| 31. #737 | D9 | semidirect |
| 73. 3−1+2 | C3⋊D9 | semidirect |
| 85. C3×C9 | C3×D9 | semidirect |
| 86. C3×C9 | C3⋊D9 | semidirect |
| 115. C9 | #4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#737 | 2 |
| C3⋊#4207 | 3 |
| C3⋊(C9⋊D9) | 3 |
| #92299 | 3 |
| #92297 | 3 |
| #92296 | 3 |
| C3×C9⋊D9 | 3 |