Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C3×D72 | C2 | semidirect |
| 2. C2×C3×C8×D9 | C2 | semidirect |
| 3. C3×#63457 | C2 | semidirect |
| 4. C3×C9×#107 | C2 | semidirect |
| 5. C3×#63369 | C2 | semidirect |
| 7. #10588563 | C3 | direct (N × H) |
| 22. C2×D72 | C2×C3 | semidirect |
| 23. C2×C8×D9 | C2×C3 | semidirect |
| 24. #63457 | C2×C3 | semidirect |
| 26. C9×#107 | C2×C3 | semidirect |
| 27. #63369 | C2×C3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 68. C2×C3×D9 | D8 | semidirect |
| 80. C3×#107 | D9 | semidirect |
| 109. C8×C9 | C3×D4 | semidirect |
| 155. C2×D9 | C3×D8 | semidirect |
| 166. #107 | C3×D9 | semidirect |
| 168. C3×C9 | #466 | semidirect |
| 193. C3×C8 | D36 | semidirect |
| 246. C9 | C3×#466 | semidirect |
| 258. C8 | C3×D36 | semidirect |
| 284. C3 | #10588563 | 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 |
| C2×C3×C8×D9 | 2 |
| C3×#63457 | 2 |
| C3×C9×#107 | 2 |
| C3×#63369 | 2 |
| C3×#4883 | 3 |
| #10588563 | 3 |