Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1595 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1595 conjugacy classes of subgroups — too many to draw. Only its 261 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. H(3,𝔽3)×C4⋊Q8 | C2 | semidirect |
| 3. #11721861 | C2 | semidirect |
| 5. #11721756 | C2 | semidirect |
| 7. #11721715 | C2 | semidirect |
| 23. C32×C4⋊Q8 | D3 | semidirect |
| 39. C4×#272 | Q8 | semidirect |
| 62. C4×H(3,𝔽3) | C2×Q8 | semidirect |
| 65. #1084 | C2×Q8 | semidirect |
| 96. #272 | C4⋊Q8 | direct (N × H) |
| 128. C32×C4 | D3×Q8 | semidirect |
| 136. C4⋊Q8 | #272 | direct (N × H) |
| 139. H(3,𝔽3) | C2×C4⋊Q8 | semidirect |
| 200. C32 | D3×C4⋊Q8 | semidirect |
| 228. C4 | Q8×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#272 | 2 |
| H(3,𝔽3)×C4⋊Q8 | 2 |
| #11721861 | 2 |
| C4⋊C4×#272 | 2 |
| #11721756 | 2 |
| C42×#272 | 2 |
| #11721715 | 2 |
| C3×D3×C4⋊Q8 | 3 |