Finite Group DatabasebetaFinite Group Databasebeta← C2×C32×(C22⋊C9)⋊C2 #13049271
Order 1296.
432 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 78 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×C32 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | C22⋊C9 | C22×C32 |
| Frattini | C3 | C2×C32×S4 |
| Fitting, socle | C23×C33 | D3 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C2×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C22⋊C9 | C2 | semidirect |
| 2. C32×(C22⋊C9)⋊C2 | C2 | direct (N × H) |
| 4. C2×C3×(C22⋊C9)⋊C2 | C3 | direct (N × H) |
| 6. C32×C22⋊C9 | C22 | semidirect |
| 13. C2×C3×C22⋊C9 | C2×C3 | semidirect |
| 14. C3×(C22⋊C9)⋊C2 | C2×C3 | direct (N × H) |
| 19. C2×(C22⋊C9)⋊C2 | C32 | direct (N × H) |
| 29. C3×C22⋊C9 | C22×C3 | semidirect |
| 33. C23×C32 | D9 | semidirect |
| 43. C2×C22⋊C9 | C2×C32 | semidirect |
| 44. (C22⋊C9)⋊C2 | C2×C32 | direct (N × H) |
| 64. C22×C32 | C2×D9 | semidirect |
| 73. C22⋊C9 | C22×C32 | semidirect |
| 79. C23×C3 | C3×D9 | semidirect |
| 96. C2×C32 | (C22⋊C9)⋊C2 | direct (N × H) |
| 113. C22×C3 | C2×C3×D9 | semidirect |
| 121. C32 | C2×(C22⋊C9)⋊C2 | direct (N × H) |
| 126. C23 | C32×D9 | semidirect |
| 138. C2×C3 | C3×(C22⋊C9)⋊C2 | direct (N × H) |
| 146. C22 | C2×C32×D9 | semidirect |
| 149. C3 | C2×C3×(C22⋊C9)⋊C2 | direct (N × H) |
| 154. C2 | C32×(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 |
|---|---|
| C2×C32×C22⋊C9 | 2 |
| C32×(C22⋊C9)⋊C2 | 2 |
| C2×C32×#67 | 3 |
| C2×C3×(C22⋊C9)⋊C2 | 3 |
| C2×C32×D9 | 4 |