Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
952 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 230 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. C3×C4×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×#97 | C2 | semidirect |
| 4. C3×#63648 | C2 | semidirect |
| 5. C3×#63644 | C2 | semidirect |
| 6. #10592410 | C3 | direct (N × H) |
| 15. C3×#3745 | C4 | semidirect |
| 17. C4×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 21. C32×#97 | D3 | semidirect |
| 22. C32×#97 | C2×C3 | semidirect |
| 23. #63648 | C2×C3 | semidirect |
| 24. #63644 | C2×C3 | semidirect |
| 32. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 35. C33×C8 | C2×C4 | semidirect |
| 53. #3745 | C3×C4 | semidirect |
| 72. C3×#97 | C3×D3 | semidirect |
| 73. C3×#97 | C3⋊D3 | semidirect |
| 86. C4⋊(C3⋊D3) | C2×C3×C4 | semidirect |
| 96. C32×C8 | C4×D3 | semidirect |
| 97. C32×C8 | C2×C3×C4 | semidirect |
| 145. #97 | C3×C3⋊D3 | semidirect |
| 146. C33 | #442 | semidirect |
| 167. C3×C8 | C3×C4×D3 | semidirect |
| 168. C3×C8 | C4×C3⋊D3 | semidirect |
| 206. C32 | #4711 | semidirect |
| 207. C32 | C3×#442 | semidirect |
| 216. C8 | C3×C4×C3⋊D3 | semidirect |
| 234. C3 | C3×#4711 | semidirect |
| 235. C3 | #10592410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| C3×C4×C4⋊(C3⋊D3) | 2 |
| C33×#97 | 2 |
| C3×#63648 | 2 |
| C3×#63644 | 2 |
| #10592410 | 3 |
| C3×#4711 | 3 |