Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
583 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 583 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11721776 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #11720552 | C2 | semidirect |
| 5. #11720522 | C2 | semidirect |
| 12. #88530 | C4 | semidirect |
| 13. #88529 | C4 | semidirect |
| 14. #88528 | C4 | semidirect |
| 19. C32×C4×C8 | D3 | semidirect |
| 106. C4×C8 | #272 | semidirect |
| 107. H(3,𝔽3) | #443 | semidirect |
| 155. C32 | #4700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721779 | 2 |
| #11721776 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720552 | 2 |
| #11720522 | 2 |
| C3×#4700 | 3 |