Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1699 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1699 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 3. C2×#88449 | C2 | direct (N × H) |
| 6. C22×#1084 | C4 | semidirect |
| 10. #88449 | C22 | direct (N × H) |
| 20. C2×#1084 | C2×C4 | semidirect |
| 37. C22×H(3,𝔽3) | C4⋊C4 | semidirect |
| 42. #1084 | C22×C4 | semidirect |
| 69. C2×H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 95. C22×C32 | Dic3⋊C4 | semidirect |
| 107. H(3,𝔽3) | C22×C4⋊C4 | semidirect |
| 136. C2×C32 | C2×Dic3⋊C4 | semidirect |
| 168. C32 | C22×Dic3⋊C4 | semidirect |
| 189. C22 | #88449 | direct (N × H) |
| 199. C2 | C2×#88449 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1084 | 2 |
| C23×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88449 | 2 |
| C22×Dic3⋊Dic3 | 3 |