Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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×C8×C3⋊D9 | C2 | semidirect |
| 2. C2×C9×D24 | C2 | semidirect |
| 3. #11721045 | C2 | semidirect |
| 4. C3×#63378 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 27. #63378 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 67. C2×C3⋊D9 | D8 | semidirect |
| 77. C2×D24 | D9 | semidirect |
| 114. C8×C9 | D12 | semidirect |
| 179. C3×C9 | #466 | semidirect |
| 206. C3×C8 | #611 | semidirect |
| 265. C9 | #4883 | semidirect |
| 277. C8 | #6195 | semidirect |
| 304. C3 | #10588837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| C2×C9×D24 | 2 |
| #11721045 | 2 |
| C3×#63378 | 2 |
| #11720294 | 2 |
| #10590844 | 3 |
| #10588837 | 3 |