Finite Group DatabasebetaFinite Group Databasebeta← C42×((C3⋊D3)⋊C3)⋊C2 #13147892
Order 1728.
1851 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 1851 conjugacy classes of subgroups — too many to draw. Only its 387 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. C42×#272 | C2 | semidirect |
| 3. C42×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. C4×#6199 | C2 | semidirect |
| 5. C4×((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 12. C4×((C3⋊D3)⋊C3)⋊C2 | C4 | direct (N × H) |
| 13. C42×H(3,𝔽3) | C22 | semidirect |
| 14. C4×#1084 | C22 | semidirect |
| 15. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 16. #88447 | C22 | semidirect |
| 18. C42×C3⋊D3 | D3 | semidirect |
| 30. C4×#272 | C2×C4 | semidirect |
| 32. C4×(C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 33. #6199 | C2×C4 | semidirect |
| 34. ((C3⋊D3)⋊C3)⋊C4 | C2×C4 | semidirect |
| 47. C32×C42 | C2×D3 | semidirect |
| 48. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 56. ((C3⋊D3)⋊C3)⋊C2 | C42 | direct (N × H) |
| 57. C4×H(3,𝔽3) | C22×C4 | semidirect |
| 58. #1084 | C22×C4 | semidirect |
| 59. (C3⋊Dic3)⋊C3 | C22×C4 | semidirect |
| 81. C4×C3⋊D3 | C4×D3 | semidirect |
| 93. #272 | C2×C42 | semidirect |
| 94. (C3⋊D3)⋊C3 | C2×C42 | semidirect |
| 129. C32×C4 | C2×C4×D3 | semidirect |
| 130. C3⋊Dic3 | C2×C4×D3 | semidirect |
| 139. H(3,𝔽3) | C22×C42 | semidirect |
| 170. C3⋊D3 | C42×D3 | semidirect |
| 183. C42 | ((C3⋊D3)⋊C3)⋊C2 | direct (N × H) |
| 205. C32 | C2×C42×D3 | semidirect |
| 231. C4 | C4×((C3⋊D3)⋊C3)⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C42×#272 | 2 |
| C42×(C3⋊D3)⋊C3 | 2 |
| C4×#6199 | 2 |
| C4×((C3⋊D3)⋊C3)⋊C4 | 2 |
| C42×D32 | 3 |