Finite Group DatabasebetaFinite Group Databasebeta← C23×(C3⋊(C3⋊C8))⋊C3 #13153547
Order 1728.
1419 conjugacy classes of subgroups; only the 692 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 692 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. C22×(C3⋊(C3⋊C8))⋊C3 | C2 | direct (N × H) |
| 3. C23×C3⋊(C3⋊C8) | C3 | semidirect |
| 8. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | direct (N × H) |
| 12. C22×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 14. C23×H(3,𝔽3) | C8 | semidirect |
| 18. (C3⋊(C3⋊C8))⋊C3 | C23 | direct (N × H) |
| 31. C2×C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 33. C22×H(3,𝔽3) | C2×C8 | semidirect |
| 46. C23×C32 | C3⋊C8 | semidirect |
| 47. C23×C32 | C3×C8 | semidirect |
| 56. C3⋊(C3⋊C8) | C23×C3 | semidirect |
| 59. C2×H(3,𝔽3) | C22×C8 | semidirect |
| 78. C22×C32 | C2×C3⋊C8 | semidirect |
| 79. C22×C32 | C2×C3×C8 | semidirect |
| 90. H(3,𝔽3) | C23×C8 | semidirect |
| 112. C2×C32 | C22×C3⋊C8 | semidirect |
| 113. C2×C32 | C22×C3×C8 | semidirect |
| 137. C32 | C23×C3⋊C8 | semidirect |
| 138. C32 | C23×C3×C8 | semidirect |
| 139. C23 | (C3⋊(C3⋊C8))⋊C3 | direct (N × H) |
| 152. C22 | C2×(C3⋊(C3⋊C8))⋊C3 | direct (N × H) |
| 160. C2 | C22×(C3⋊(C3⋊C8))⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×H(3,𝔽3) | 2 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C23×C3⋊(C3⋊C8) | 3 |
| C23×C3×C3⋊C8 | 3 |