Finite Group DatabasebetaFinite Group Databasebeta← C22×(C3⋊(C3⋊C16))⋊C3 #13143110
Order 1728.
419 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 419 conjugacy classes of subgroups — too many to draw. Only its 212 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 | direct (N × H) |
| 3. C22×C3⋊(C3⋊C16) | C3 | semidirect |
| 8. (C3⋊(C3⋊C16))⋊C3 | C22 | direct (N × H) |
| 12. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 31. C3⋊(C3⋊C16) | C22×C3 | semidirect |
| 33. C22×H(3,𝔽3) | C16 | semidirect |
| 60. C2×H(3,𝔽3) | C2×C16 | semidirect |
| 79. C22×C32 | C3⋊C16 | semidirect |
| 80. C22×C32 | C3×C16 | semidirect |
| 91. H(3,𝔽3) | C22×C16 | semidirect |
| 114. C2×C32 | C2×C3⋊C16 | semidirect |
| 115. C2×C32 | C2×C3×C16 | semidirect |
| 139. C32 | C22×C3⋊C16 | semidirect |
| 140. C32 | C22×C3×C16 | semidirect |
| 154. C22 | (C3⋊(C3⋊C16))⋊C3 | direct (N × H) |
| 162. C2 | C2×(C3⋊(C3⋊C16))⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×H(3,𝔽3) | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| C22×C3⋊(C3⋊C16) | 3 |
| C22×C3×C3⋊C16 | 3 |