Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 125 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×C16×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#88386 | C2 | semidirect |
| 4. #11720511 | C2 | direct (N × H) |
| 11. C16×H(3,𝔽3) | C22 | semidirect |
| 12. #88386 | C22 | semidirect |
| 14. C2×C32×C16 | D3 | semidirect |
| 32. C32×C16 | C2×D3 | semidirect |
| 57. C2×H(3,𝔽3) | M32 | semidirect |
| 83. C2×C16 | #272 | semidirect |
| 84. H(3,𝔽3) | C2×M32 | semidirect |
| 101. C2×C32 | #798 | semidirect |
| 110. C16 | C2×#272 | semidirect |
| 123. C32 | C2×#798 | semidirect |
| 147. C2 | #11720511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| C2×#88386 | 2 |
| #11720511 | 2 |
| C2×C3×#798 | 3 |