Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
259 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 259 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. C2×#88386 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 15. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 50. C2×(C3⋊D3)⋊C3 | C16 | semidirect |
| 116. C2×C3⋊D3 | C3⋊C16 | semidirect |
| 131. H(3,𝔽3) | C22⋊C16 | semidirect |
| 202. C32 | (C2×D3)⋊C16 | semidirect |
| 203. C32 | #4549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C2×#88386 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589108 | 3 |
| (C2×D3)⋊(C3⋊C16) | 3 |