Finite Group DatabasebetaFinite Group Databasebeta← C22×((C22⋊C9)⋊C2)⋊C3 #11724043
Order 864.
489 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 62 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 | ((C22⋊C9)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊C9 | C23×C3 |
| Frattini | C3 | C22×C3×S4 |
| Fitting | C24×C32 | D3 |
| socle | C24×C3 | C3×D3 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#1094 | C2 | semidirect |
| 2. C2×((C22⋊C9)⋊C2)⋊C3 | C2 | direct (N × H) |
| 4. C22×(C22⋊C9)⋊C2 | C3 | semidirect |
| 6. C2×#1094 | C22 | semidirect |
| 7. ((C22⋊C9)⋊C2)⋊C3 | C22 | direct (N × H) |
| 14. C22×C22⋊C9 | C2×C3 | semidirect |
| 15. C2×(C22⋊C9)⋊C2 | C2×C3 | semidirect |
| 18. #1094 | C23 | semidirect |
| 32. C2×C22⋊C9 | C22×C3 | semidirect |
| 33. (C22⋊C9)⋊C2 | C22×C3 | semidirect |
| 60. C22⋊C9 | C23×C3 | semidirect |
| 91. C24 | AGL(1,ℤ/9) | semidirect |
| 126. C23 | C2×AGL(1,ℤ/9) | semidirect |
| 147. C22 | ((C22⋊C9)⋊C2)⋊C3 | direct (N × H) |
| 148. C22 | C22×AGL(1,ℤ/9) | semidirect |
| 155. C2 | C2×((C22⋊C9)⋊C2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1094 | 2 |
| C2×((C22⋊C9)⋊C2)⋊C3 | 2 |
| C22×C3×#67 | 3 |
| C22×(C22⋊C9)⋊C2 | 3 |
| C22×AGL(1,ℤ/9) | 4 |