Finite Group DatabasebetaFinite Group Databasebeta← C22×C3⋊((C22⋊C9)⋊C2) #11724047
Order 864.
722 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C23 |
| Frattini | C3 | C22×C3⋊S4 |
| Fitting, socle | C24×C32 | D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C22⋊C9 | C2 | semidirect |
| 2. C2×C3⋊((C22⋊C9)⋊C2) | C2 | direct (N × H) |
| 6. C2×C3×C22⋊C9 | C22 | semidirect |
| 7. C3⋊((C22⋊C9)⋊C2) | C22 | direct (N × H) |
| 13. C22×C22⋊C9 | D3 | semidirect |
| 17. C3×C22⋊C9 | C23 | semidirect |
| 30. C2×C22⋊C9 | C2×D3 | semidirect |
| 34. C24×C3 | D9 | semidirect |
| 56. C22⋊C9 | C22×D3 | semidirect |
| 63. C23×C3 | C2×D9 | semidirect |
| 84. C24 | C3⋊D9 | semidirect |
| 96. C22×C3 | (C22⋊C9)⋊C2 | semidirect |
| 97. C22×C3 | C22×D9 | semidirect |
| 115. C23 | C2×C3⋊D9 | semidirect |
| 123. C2×C3 | C2×(C22⋊C9)⋊C2 | semidirect |
| 134. C22 | C3⋊((C22⋊C9)⋊C2) | direct (N × H) |
| 135. C22 | C22×C3⋊D9 | semidirect |
| 137. C3 | C22×(C22⋊C9)⋊C2 | semidirect |
| 142. C2 | C2×C3⋊((C22⋊C9)⋊C2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C9 | 2 |
| C2×C3⋊((C22⋊C9)⋊C2) | 2 |
| C22×#638 | 3 |
| C22×(C22⋊C9)⋊C2 | 3 |
| C22×C3⋊D9 | 4 |