Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
605 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×#3754⋊C3 | C2 | semidirect |
| 3. #64078⋊C3 | C2 | semidirect |
| 4. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 5. #10592775 | C3 | semidirect |
| 17. C2×#3754 | C2×C3 | semidirect |
| 18. #64078 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 30. (C3⋊(C3⋊C8))⋊C3 | D4 | semidirect |
| 54. C4×H(3,𝔽3) | SD16 | semidirect |
| 89. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 130. C32×C4 | #214 | semidirect |
| 131. C32×C4 | C3×SD16 | semidirect |
| 140. H(3,𝔽3) | #492 | semidirect |
| 210. C32 | #5076 | semidirect |
| 211. C32 | C3×#492 | semidirect |
| 236. C4 | #3754⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#127 | 2 |
| C2×#3754⋊C3 | 2 |
| #64078⋊C3 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #10592775 | 3 |
| C3×#5076 | 3 |