Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
507 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. C4×#1088 | C4 | semidirect |
| 10. #88590 | C4 | direct (N × H) |
| 38. #1088 | C42 | semidirect |
| 39. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 40. #1084 | C4⋊C4 | semidirect |
| 88. H(3,𝔽3) | C4×C4⋊C4 | semidirect |
| 174. C4 | #88590 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1088 | 2 |
| C2×#88590 | 2 |
| C4×#6199 | 2 |
| #11720707 | 2 |
| C4×C4⋊Dic3 | 9 |