Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
541 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 541 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×#3744⋊C3 | C2 | semidirect |
| 3. #64078⋊C3 | C2 | semidirect |
| 4. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 5. #10592392 | C3 | semidirect |
| 14. C2×#3744 | C2×C3 | semidirect |
| 16. #64078 | C2×C3 | semidirect |
| 21. C32×C4×C8 | D3 | semidirect |
| 22. C32×C4×C8 | C2×C3 | semidirect |
| 30. C8×H(3,𝔽3) | D4 | semidirect |
| 53. C4×H(3,𝔽3) | SD16 | semidirect |
| 86. C32×C8 | D12 | semidirect |
| 87. C32×C8 | C3×D4 | semidirect |
| 124. C32×C4 | #204 | semidirect |
| 125. C32×C4 | C3×SD16 | semidirect |
| 133. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 134. H(3,𝔽3) | #492 | semidirect |
| 199. C32 | #4693 | semidirect |
| 200. C32 | C3×#492 | semidirect |
| 208. C8 | C4⋊((C3⋊D3)⋊C3) | semidirect |
| 224. C4 | #3744⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744⋊C3 | 2 |
| #11721385 | 2 |
| #64078⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #10592392 | 3 |
| C3×#4693 | 3 |