Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
6454 conjugacy classes of subgroups; only the 670 normal subgroups are shown.
This group has 6454 conjugacy classes of subgroups — too many to draw. Only its 670 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. C23×#1094 | C2 | direct (N × H) |
| 3. C24×C22⋊C9 | C3 | semidirect |
| 5. C22×#1094 | C22 | direct (N × H) |
| 9. C23×C22⋊C9 | C2×C3 | semidirect |
| 11. C2×#1094 | C23 | direct (N × H) |
| 21. C22×C22⋊C9 | C22×C3 | semidirect |
| 23. #1094 | C24 | direct (N × H) |
| 37. C2×C22⋊C9 | C23×C3 | semidirect |
| 38. C26 | 3−1+2 | semidirect |
| 59. C22⋊C9 | C24×C3 | semidirect |
| 62. C25 | C2×3−1+2 | semidirect |
| 84. C24 | #1094 | direct (N × H) |
| 85. C24 | C22×3−1+2 | semidirect |
| 104. C23 | C2×#1094 | direct (N × H) |
| 105. C23 | C23×3−1+2 | semidirect |
| 116. C22 | C22×#1094 | direct (N × H) |
| 117. C22 | C24×3−1+2 | semidirect |
| 122. C2 | C23×#1094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1094 | 2 |
| C26×C32 | 3 |
| C24×C22⋊C9 | 3 |
| C24×3−1+2 | 4 |