Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊((C22⋊C27)⋊C2) #13145293
Order 1728.
591 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C22×(C22⋊C27)⋊C2 | C2 | semidirect |
| 2. C2×C4×C22⋊C27 | C2 | semidirect |
| 3. C4⋊((C22⋊C27)⋊C2) | C2 | direct (N × H) |
| 7. C2×(C22⋊C27)⋊C2 | C22 | semidirect |
| 9. C4×C22⋊C27 | C22 | semidirect |
| 18. C2×C22⋊C27 | D4 | semidirect |
| 44. C22⋊C27 | C2×D4 | semidirect |
| 116. C23×C4 | D27 | semidirect |
| 165. C22×C4 | C2×D27 | semidirect |
| 194. C23 | D108 | semidirect |
| 208. C2×C4 | (C22⋊C27)⋊C2 | semidirect |
| 227. C22 | C2×D108 | semidirect |
| 231. C4 | C2×(C22⋊C27)⋊C2 | semidirect |
| 237. 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 |
| C4⋊((C22⋊C27)⋊C2) | 2 |
| C2×#63492 | 3 |
| C2×D108 | 4 |