Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
770 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 137 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. C4×D4×H(3,𝔽3) | C2 | semidirect |
| 2. C2×#88545 | C2 | semidirect |
| 3. #11721720 | C2 | semidirect |
| 4. #11720531 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 17. C32×C4×D4 | D3 | semidirect |
| 25. D4×H(3,𝔽3) | D4 | semidirect |
| 57. C4×H(3,𝔽3) | D8 | semidirect |
| 73. C32×D4 | D12 | semidirect |
| 119. C32×C4 | #213 | semidirect |
| 124. C4×D4 | #272 | semidirect |
| 127. H(3,𝔽3) | #459 | semidirect |
| 195. C32 | #5015 | semidirect |
| 203. D4 | C4⋊#272 | semidirect |
| 229. C4 | #88545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| C2×#88545 | 2 |
| #11721720 | 2 |
| #11720531 | 2 |
| C4⋊#6180 | 2 |
| C3×#5015 | 3 |