Finite Group DatabasebetaFinite Group Databasebeta← (C2×(C22⋊C27)⋊C2)⋊C4 #13136151
Order 1728.
361 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 361 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
| 8. C2×(C22⋊C27)⋊C2 | C4 | semidirect |
| 51. C22⋊C27 | C22⋊C4 | semidirect |
| 144. C23×C4 | D27 | semidirect |
| 269. C2×C4 | (C22⋊C27)⋊C2 | semidirect |
| 295. C22 | (C2×D27)⋊C4 | semidirect |
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 |
| #10588893 | 3 |
| (C2×D27)⋊C4 | 4 |