Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
391 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 3. #11720252 | C2 | direct (N × H) |
| 10. (C3⋊(C3⋊C16))⋊C3 | C22 | semidirect |
| 13. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 36. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 69. C2×H(3,𝔽3) | M32 | semidirect |
| 105. H(3,𝔽3) | C2×M32 | semidirect |
| 132. C2×C32 | #798 | semidirect |
| 161. C32 | C2×#798 | semidirect |
| 189. C2 | #11720252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #11720252 | 2 |
| C2×#63543 | 3 |