Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
737 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 237 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. C22×#6180 | C2 | semidirect |
| 3. #11720573 | C2 | semidirect |
| 4. C4⋊#6180 | C2 | semidirect |
| 5. C4×#6180 | C2 | semidirect |
| 22. D4×H(3,𝔽3) | C8 | semidirect |
| 31. #6180 | D4 | direct (N × H) |
| 45. C22×H(3,𝔽3) | C2×C8 | semidirect |
| 49. C4×H(3,𝔽3) | C2×C8 | semidirect |
| 63. C32×D4 | C3⋊C8 | semidirect |
| 98. C22×C32 | C2×C3⋊C8 | semidirect |
| 102. C32×C4 | C2×C3⋊C8 | semidirect |
| 110. H(3,𝔽3) | C8×D4 | semidirect |
| 164. C32 | D4×C3⋊C8 | semidirect |
| 166. D4 | #6180 | direct (N × H) |
| 186. C22 | C2×#6180 | semidirect |
| 190. C4 | C2×#6180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| C22×#6180 | 2 |
| #11720573 | 2 |
| C4⋊#6180 | 2 |
| C4×#6180 | 2 |
| C3×D4×C3⋊C8 | 3 |