Finite Group DatabasebetaFinite Group Databasebeta← C22×((C3⋊D3)⋊C3)⋊C4 #11722537
Order 864.
880 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 244 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 |
|---|---|---|
| 2. C22×#1084 | C2 | semidirect |
| 3. C22×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C2×((C3⋊D3)⋊C3)⋊C4 | C2 | direct (N × H) |
| 8. C22×(C3⋊D3)⋊C3 | C4 | semidirect |
| 10. C2×#1084 | C22 | semidirect |
| 11. C2×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 12. ((C3⋊D3)⋊C3)⋊C4 | C22 | direct (N × H) |
| 15. C22×C3⋊Dic3 | D3 | semidirect |
| 22. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 24. C2×(C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 26. #1084 | C23 | semidirect |
| 27. (C3⋊Dic3)⋊C3 | C23 | semidirect |
| 34. C22×C3⋊D3 | Dic3 | semidirect |
| 38. C2×C3⋊Dic3 | C2×D3 | semidirect |
| 45. C2×H(3,𝔽3) | C22×C4 | semidirect |
| 47. (C3⋊D3)⋊C3 | C22×C4 | semidirect |
| 63. C22×C32 | C4×D3 | semidirect |
| 64. C22×C32 | C2×Dic3 | semidirect |
| 67. C2×C3⋊D3 | C2×Dic3 | semidirect |
| 71. C3⋊Dic3 | C22×D3 | semidirect |
| 77. H(3,𝔽3) | C23×C4 | semidirect |
| 100. C2×C32 | C2×C4×D3 | semidirect |
| 101. C2×C32 | C22×Dic3 | semidirect |
| 104. C3⋊D3 | C22×Dic3 | semidirect |
| 132. C32 | C22×C4×D3 | semidirect |
| 133. C32 | C23×Dic3 | semidirect |
| 153. C22 | ((C3⋊D3)⋊C3)⋊C4 | direct (N × H) |
| 162. C2 | C2×((C3⋊D3)⋊C3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×(C3⋊D3)⋊C3 | 2 |
| C22×#1084 | 2 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C4 | 2 |
| C22×#624 | 3 |
| C22×D3×Dic3 | 3 |