Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1111 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1111 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 1. C22×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. #11720574 | C2 | semidirect |
| 10. C22×C32×Q8 | D3 | semidirect |
| 16. C22×#272 | Q8 | semidirect |
| 75. C22×Q8 | #272 | semidirect |
| 78. H(3,𝔽3) | #393 | semidirect |
| 122. C32 | #5231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×H(3,𝔽3) | 2 |
| C2×#88542 | 2 |
| #11720574 | 2 |
| C3×#5231 | 3 |