Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
235 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C42⋊C3 |
| commutator, Fitting, cosocle, hypocenter | C9×#95 | C2×C3 |
| Frattini, socle | C23×C3 | D3×A4 |
| LCS | G ▷ C9×#95 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#95⋊C3 | C2 | semidirect |
| 3. D9×#95 | C3 | semidirect |
| 7. C9×#95 | C2×C3 | semidirect |
| 27. #95⋊C3 | D9 | direct (N × H) |
| 68. #95 | C3×D9 | semidirect |
| 91. D9 | #95⋊C3 | direct (N × H) |
| 114. C9 | C2×#95⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#95⋊C3 | 2 |
| D3×#95⋊C3 | 3 |
| D9×#95 | 3 |
| C2×A4×D9 | 4 |