Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1792 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 1. C33×C4×Q8 | C2 | semidirect |
| 2. C2×#88862 | C2 | semidirect |
| 4. #11722179 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 17. C32×C4×Q8 | D3 | semidirect |
| 24. C33×Q8 | D4 | semidirect |
| 53. C33×C4 | SD16 | semidirect |
| 56. C3×C4×Q8 | C3⋊D3 | semidirect |
| 63. C32×Q8 | D12 | semidirect |
| 96. C32×C4 | #215 | semidirect |
| 101. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 104. C33 | #460 | semidirect |
| 107. C3×Q8 | C4⋊(C3⋊D3) | semidirect |
| 139. C3×C4 | #3755 | semidirect |
| 142. C32 | #5027 | semidirect |
| 145. Q8 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 167. C4 | #88862 | semidirect |
| 170. C3 | #10592726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| C2×#88862 | 2 |
| #11723915 | 2 |
| #11722179 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592726 | 3 |