Finite Group DatabasebetaFinite Group Databasebeta← C2×C4×(C22⋊C27)⋊C2 #13145292
Order 1728.
591 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 75 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×C4×C22⋊C27 | C2 | semidirect |
| 3. C2×(C22⋊C27)⋊C4 | C2 | semidirect |
| 4. C4×(C22⋊C27)⋊C2 | C2 | direct (N × H) |
| 7. C2×(C22⋊C27)⋊C2 | C4 | direct (N × H) |
| 10. C4×C22⋊C27 | C22 | semidirect |
| 11. (C22⋊C27)⋊C4 | C22 | semidirect |
| 22. C2×C22⋊C27 | C2×C4 | semidirect |
| 24. (C22⋊C27)⋊C2 | C2×C4 | direct (N × H) |
| 54. C22⋊C27 | C22×C4 | semidirect |
| 141. C23×C4 | D27 | semidirect |
| 199. C22×C4 | C2×D27 | semidirect |
| 233. C23 | C4×D27 | semidirect |
| 252. C2×C4 | (C22⋊C27)⋊C2 | direct (N × H) |
| 271. C22 | C2×C4×D27 | semidirect |
| 277. C4 | C2×(C22⋊C27)⋊C2 | direct (N × H) |
| 283. C2 | C4×(C22⋊C27)⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C22⋊C27)⋊C2 | 2 |
| C2×C4×C22⋊C27 | 2 |
| C2×(C22⋊C27)⋊C4 | 2 |
| C4×(C22⋊C27)⋊C2 | 2 |
| C2×C4×#611 | 3 |
| C2×C4×D27 | 4 |