Finite Group DatabasebetaFinite Group Databasebeta← C8×((C3⋊D3)⋊C3)⋊C4 #13138770
Order 1728.
611 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 611 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 4. C8×#1084 | C2 | semidirect |
| 5. C8×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 6. #11720310 | C2 | semidirect |
| 7. #11720302 | C2 | semidirect |
| 18. C8×(C3⋊D3)⋊C3 | C4 | semidirect |
| 20. ((C3⋊D3)⋊C3)⋊C8 | C4 | semidirect |
| 27. C8×C3⋊Dic3 | D3 | semidirect |
| 43. ((C3⋊D3)⋊C3)⋊C4 | C8 | direct (N × H) |
| 44. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 45. #6180 | C2×C4 | semidirect |
| 46. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 47. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 61. C8×C3⋊D3 | Dic3 | semidirect |
| 81. #1084 | C2×C8 | semidirect |
| 83. (C3⋊Dic3)⋊C3 | C2×C8 | semidirect |
| 125. C32×C8 | C4×D3 | semidirect |
| 126. C32×C8 | C2×Dic3 | semidirect |
| 127. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 128. C3⋊(C3⋊C8) | C2×Dic3 | semidirect |
| 137. (C3⋊D3)⋊C3 | C4×C8 | semidirect |
| 187. C3⋊Dic3 | D3×C8 | semidirect |
| 201. H(3,𝔽3) | C2×C4×C8 | semidirect |
| 248. C3⋊D3 | C8×Dic3 | semidirect |
| 290. C32 | C4×D3×C8 | semidirect |
| 291. C32 | C2×C8×Dic3 | semidirect |
| 303. C8 | ((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 |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C4×((C3⋊D3)⋊C3)⋊C4 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C8 | 2 |
| C8×#1084 | 2 |
| C8×(C3⋊Dic3)⋊C3 | 2 |
| #11720310 | 2 |
| #11720302 | 2 |
| C8×#624 | 3 |
| D3×C8×Dic3 | 3 |