Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
473 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11720580 | C2 | semidirect |
| 5. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 7. C42×H(3,𝔽3) | C4 | semidirect |
| 22. C2×C32×D4 | Dic3 | semidirect |
| 24. C32×C42 | Dic3 | semidirect |
| 71. H(3,𝔽3) | #353 | semidirect |
| 93. C2×D4 | #1084 | semidirect |
| 96. C42 | #1084 | semidirect |
| 113. C32 | #4545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#127 | 2 |
| #11720580 | 2 |
| C3×#4545 | 3 |