Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
616 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 116 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. C32×#912 | C2 | semidirect |
| 2. #11723337 | C2 | semidirect |
| 3. #11722196 | C2 | semidirect |
| 4. C3×#63654 | C2 | semidirect |
| 5. #11722013 | C2 | semidirect |
| 6. #11722010 | C2 | semidirect |
| 7. D3×C3⋊(C3⋊C16) | C2 | semidirect |
| 23. C3×#912 | D3 | semidirect |
| 27. #63654 | D3 | semidirect |
| 83. #912 | C3⋊D3 | semidirect |
| 175. C33 | #508 | semidirect |
| 241. C32 | #4916 | semidirect |
| 242. C32 | #5194 | semidirect |
| 273. C3 | #10591034 | semidirect |
| 274. C3 | #10592893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#912 | 2 |
| #11723337 | 2 |
| #11722196 | 2 |
| C3×#63654 | 2 |
| #11722013 | 2 |
| #11722010 | 2 |
| D3×C3⋊(C3⋊C16) | 2 |
| #10592893 | 3 |
| #10591034 | 3 |