Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
676 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 203 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×D108 | C2 | semidirect |
| 2. C22×C8×C27 | C2 | semidirect |
| 3. C2×D216 | C2 | direct (N × H) |
| 8. C2×D108 | C22 | semidirect |
| 9. C2×C8×C27 | C22 | semidirect |
| 10. D216 | C22 | direct (N × H) |
| 20. D108 | C23 | semidirect |
| 21. C8×C27 | C23 | semidirect |
| 29. C22×C27 | D8 | semidirect |
| 47. C2×C27 | C2×D8 | semidirect |
| 64. C22×C8 | D27 | semidirect |
| 65. C27 | C22×D8 | semidirect |
| 82. C2×C8 | C2×D27 | semidirect |
| 97. C8 | C22×D27 | semidirect |
| 103. C22 | D216 | direct (N × H) |
| 109. C2 | C2×D216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D108 | 2 |
| C22×C8×C27 | 2 |
| C2×D216 | 2 |
| C22×D72 | 3 |