Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
605 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 103 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. #64078⋊C3 | C2 | semidirect |
| 3. C2×#88437 | C2 | semidirect |
| 4. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 14. #64078 | D3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 30. (C3⋊(C3⋊C8))⋊C3 | D4 | semidirect |
| 54. C4×H(3,𝔽3) | SD16 | semidirect |
| 89. C3⋊(C3⋊C8) | D12 | semidirect |
| 130. C32×C4 | #204 | semidirect |
| 131. C32×C4 | #215 | semidirect |
| 140. H(3,𝔽3) | #492 | semidirect |
| 210. C32 | #4693 | semidirect |
| 211. C32 | #5085 | semidirect |
| 236. C4 | #88437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721720 | 2 |
| #64078⋊C3 | 2 |
| C2×#88437 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #10590375 | 3 |
| #10590369 | 3 |