Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 134 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×D36 | C2 | semidirect |
| 3. C3×C9×#97 | C2 | semidirect |
| 4. C3×#63380 | C2 | semidirect |
| 5. C3×#63377 | C2 | semidirect |
| 7. #10588392 | C3 | direct (N × H) |
| 15. C3×D72 | C4 | semidirect |
| 22. C4×D36 | C2×C3 | semidirect |
| 24. C9×#97 | C2×C3 | semidirect |
| 25. #63380 | C2×C3 | semidirect |
| 26. #63377 | C2×C3 | semidirect |
| 32. C3×D36 | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 56. D72 | C3×C4 | semidirect |
| 72. C3×#97 | D9 | semidirect |
| 92. D36 | C2×C3×C4 | semidirect |
| 97. C8×C9 | C2×C3×C4 | semidirect |
| 145. #97 | C3×D9 | semidirect |
| 146. C3×C9 | #442 | semidirect |
| 167. C3×C8 | C4×D9 | semidirect |
| 207. C9 | C3×#442 | semidirect |
| 216. C8 | C3×C4×D9 | semidirect |
| 234. C3 | #10588392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C3×C4×D36 | 2 |
| C3×C9×#97 | 2 |
| C3×#63380 | 2 |
| C3×#63377 | 2 |
| C3×#4711 | 3 |
| #10588392 | 3 |