Finite Group DatabasebetaFinite Group Databasebeta← C22×((C3⋊D3)⋊C3)⋊C8 #13150587
Order 1728.
1259 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 1259 conjugacy classes of subgroups — too many to draw. Only its 379 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×#6180 | C2 | semidirect |
| 3. C22×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. C2×((C3⋊D3)⋊C3)⋊C8 | C2 | direct (N × H) |
| 12. C2×#6180 | C22 | semidirect |
| 13. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 14. ((C3⋊D3)⋊C3)⋊C8 | C22 | direct (N × H) |
| 17. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 25. C22×(C3⋊D3)⋊C3 | C8 | semidirect |
| 32. #6180 | C23 | semidirect |
| 33. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 48. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 55. C22×H(3,𝔽3) | C2×C8 | semidirect |
| 57. C2×(C3⋊D3)⋊C3 | C2×C8 | semidirect |
| 78. C22×C3⋊D3 | C3⋊C8 | semidirect |
| 94. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 100. C2×H(3,𝔽3) | C22×C8 | semidirect |
| 102. (C3⋊D3)⋊C3 | C22×C8 | semidirect |
| 131. C22×C32 | D3×C8 | semidirect |
| 132. C22×C32 | C2×C3⋊C8 | semidirect |
| 135. C2×C3⋊D3 | C2×C3⋊C8 | semidirect |
| 151. H(3,𝔽3) | C23×C8 | semidirect |
| 188. C2×C32 | C2×D3×C8 | semidirect |
| 189. C2×C32 | C22×C3⋊C8 | semidirect |
| 192. C3⋊D3 | C22×C3⋊C8 | semidirect |
| 228. C32 | C22×D3×C8 | semidirect |
| 229. C32 | C23×C3⋊C8 | semidirect |
| 253. C22 | ((C3⋊D3)⋊C3)⋊C8 | direct (N × H) |
| 263. C2 | C2×((C3⋊D3)⋊C3)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×(C3⋊D3)⋊C3 | 2 |
| C22×#6180 | 2 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C8 | 2 |
| C22×#3710 | 3 |
| C22×D3×C3⋊C8 | 3 |