Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1284 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 246 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×C3×#3754 | C2 | semidirect |
| 3. C3×#64078 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10592775 | C3 | direct (N × H) |
| 17. C2×#3754 | C2×C3 | semidirect |
| 18. #64078 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 30. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 53. C33×C4 | SD16 | semidirect |
| 84. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 118. C32×C4 | #214 | semidirect |
| 119. C32×C4 | C3×SD16 | semidirect |
| 128. C33 | #492 | semidirect |
| 178. C3×C4 | C3×#214 | semidirect |
| 179. C3×C4 | #3754 | semidirect |
| 184. C32 | #5076 | semidirect |
| 185. C32 | C3×#492 | semidirect |
| 207. C4 | C3×#3754 | semidirect |
| 210. C3 | C3×#5076 | semidirect |
| 211. C3 | #10592775 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#127 | 2 |
| C2×C3×#3754 | 2 |
| C3×#64078 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592775 | 3 |
| C3×#5076 | 3 |