Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 113 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)×M32 | C2 | semidirect |
| 3. #11720545 | C2 | semidirect |
| 4. #11720511 | C2 | semidirect |
| 5. C16×#272 | C2 | semidirect |
| 14. C16×H(3,𝔽3) | C22 | semidirect |
| 15. #88386 | C22 | semidirect |
| 17. C32×M32 | D3 | semidirect |
| 41. C32×C16 | C2×D3 | semidirect |
| 76. #272 | M32 | direct (N × H) |
| 106. M32 | #272 | direct (N × H) |
| 108. H(3,𝔽3) | C2×M32 | semidirect |
| 143. C16 | C2×#272 | semidirect |
| 160. C32 | D3×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| H(3,𝔽3)×M32 | 2 |
| #11720545 | 2 |
| #11720511 | 2 |
| C16×#272 | 2 |
| C3×D3×M32 | 3 |