Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4172 conjugacy classes of subgroups; only the 1001 normal subgroups are shown.
This group has 4172 conjugacy classes of subgroups — too many to draw. Only its 1001 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. C33×C4×Q8 | C2 | semidirect |
| 3. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #11723928 | C2 | semidirect |
| 7. C4×#6308 | C2 | semidirect |
| 10. Q8×C3⋊(C3⋊D3) | C4 | direct (N × H) |
| 23. C32×C4×Q8 | D3 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 39. C4×C3⋊(C3⋊D3) | Q8 | direct (N × H) |
| 40. #6308 | C2×C4 | semidirect |
| 61. C33×C4 | C2×Q8 | semidirect |
| 64. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 66. C3×C4×Q8 | C3⋊D3 | semidirect |
| 73. C32×Q8 | C4×D3 | semidirect |
| 88. C3⋊(C3⋊D3) | C4×Q8 | direct (N × H) |
| 108. C32×C4 | D3×Q8 | semidirect |
| 116. C4×Q8 | C3⋊(C3⋊D3) | direct (N × H) |
| 119. C33 | C2×C4×Q8 | semidirect |
| 121. C3×Q8 | C4×C3⋊D3 | semidirect |
| 155. C3×C4 | Q8×C3⋊D3 | semidirect |
| 159. C32 | C4×D3×Q8 | semidirect |
| 162. Q8 | C4×C3⋊(C3⋊D3) | direct (N × H) |
| 185. C4 | Q8×C3⋊(C3⋊D3) | direct (N × H) |
| 186. C3 | C4×Q8×C3⋊D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C33×C4×Q8 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| #11723928 | 2 |
| C42×C3⋊(C3⋊D3) | 2 |
| C4×#6308 | 2 |
| C4×Q8×C3⋊D3 | 3 |