Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
781 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 781 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#88528 | C2 | semidirect |
| 3. #11721715 | C2 | semidirect |
| 4. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 16. C32×C4×C8 | D3 | semidirect |
| 24. C8×H(3,𝔽3) | D4 | semidirect |
| 37. C4×H(3,𝔽3) | SD16 | semidirect |
| 55. C32×C8 | D12 | semidirect |
| 77. C32×C4 | #204 | semidirect |
| 83. C4×C8 | #272 | semidirect |
| 84. H(3,𝔽3) | #492 | semidirect |
| 123. C32 | #4693 | semidirect |
| 131. C8 | C4⋊#272 | semidirect |
| 142. C4 | #88528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88528 | 2 |
| #11721720 | 2 |
| #11721715 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| C3×#4693 | 3 |