Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊((C3⋊Dic3)⋊C3) #11721596
Order 864.
376 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4⋊((C3⋊Dic3)⋊C3) | C2 | direct (N × H) |
| 4. C2×C4⋊(C3⋊Dic3) | C3 | semidirect |
| 7. C2×C4×H(3,𝔽3) | C4 | semidirect |
| 16. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 22. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 32. C2×C32×C4 | Dic3 | semidirect |
| 33. C2×C32×C4 | C3×C4 | semidirect |
| 40. C2×H(3,𝔽3) | C4⋊C4 | semidirect |
| 67. C32×C4 | C2×Dic3 | semidirect |
| 68. C32×C4 | C2×C3×C4 | semidirect |
| 72. H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 95. C2×C32 | C4⋊Dic3 | semidirect |
| 96. C2×C32 | C3×C4⋊C4 | semidirect |
| 130. C32 | C2×C4⋊Dic3 | semidirect |
| 131. C32 | C2×C3×C4⋊C4 | semidirect |
| 135. C2×C4 | (C3⋊Dic3)⋊C3 | semidirect |
| 158. C4 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 163. C2 | C4⋊((C3⋊Dic3)⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×H(3,𝔽3) | 2 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×C4⋊(C3⋊Dic3) | 3 |
| C2×C3×C4⋊Dic3 | 3 |