Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
891 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 891 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4⋊#1084 | C2 | semidirect |
| 3. C2×#88538 | C2 | semidirect |
| 4. #11720583 | C2 | semidirect |
| 5. #11720578 | C2 | semidirect |
| 8. #41×H(3,𝔽3) | C4 | semidirect |
| 27. Q8×H(3,𝔽3) | C2×C4 | semidirect |
| 30. D4×H(3,𝔽3) | C2×C4 | semidirect |
| 43. C32×#41 | Dic3 | semidirect |
| 79. C32×Q8 | C2×Dic3 | semidirect |
| 82. C32×D4 | C2×Dic3 | semidirect |
| 139. H(3,𝔽3) | #417 | semidirect |
| 178. #41 | #1084 | semidirect |
| 213. C32 | #5232 | semidirect |
| 217. Q8 | C2×#1084 | semidirect |
| 220. D4 | C2×#1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×H(3,𝔽3) | 2 |
| C2×C4⋊#1084 | 2 |
| C2×#88538 | 2 |
| #11720583 | 2 |
| #11720578 | 2 |
| C3×#5232 | 3 |