Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
737 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 153 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×C8×#272 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #11720553 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 18. C32×C4×C8 | D3 | semidirect |
| 26. C4⋊#272 | C8 | direct (N × H) |
| 30. C8×H(3,𝔽3) | D4 | semidirect |
| 46. C2×#272 | C2×C8 | semidirect |
| 48. C4×H(3,𝔽3) | C2×C8 | semidirect |
| 71. C32×C8 | D12 | semidirect |
| 101. C32×C4 | D3×C8 | semidirect |
| 109. C4×C8 | #272 | semidirect |
| 110. H(3,𝔽3) | C8×D4 | semidirect |
| 164. C32 | C8×D12 | semidirect |
| 175. C8 | C4⋊#272 | direct (N × H) |
| 190. C4 | C8×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C4×C4⋊#272 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720553 | 2 |
| C4⋊#6180 | 2 |
| C3×C8×D12 | 3 |