Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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×C9×D24 | C2 | semidirect |
| 2. C2×C3×C8×D9 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. #11720541 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 24. C2×C8×D9 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 68. C2×C3×D9 | D8 | semidirect |
| 77. C2×D24 | D9 | semidirect |
| 109. C8×C9 | #67 | semidirect |
| 155. C2×D9 | D24 | semidirect |
| 168. C3×C9 | #466 | semidirect |
| 193. C3×C8 | #611 | semidirect |
| 246. C9 | #5115 | semidirect |
| 258. C8 | #6194 | semidirect |
| 284. C3 | #10588837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C2×C3×C8×D9 | 2 |
| #11721036 | 2 |
| #11720541 | 2 |
| #11720295 | 2 |
| #10590831 | 3 |
| #10588837 | 3 |