Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
600 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 600 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×#919 | C2 | semidirect |
| 2. #11723336 | C2 | semidirect |
| 3. #11722199 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. #11722009 | C2 | semidirect |
| 6. #11722004 | C2 | semidirect |
| 7. D3×C3⋊(C3⋊C16) | C2 | semidirect |
| 23. C3×#919 | D3 | semidirect |
| 28. #63655 | D3 | semidirect |
| 82. #919 | C3⋊D3 | semidirect |
| 175. C33 | #508 | semidirect |
| 239. C32 | #4916 | semidirect |
| 240. C32 | #5194 | semidirect |
| 269. C3 | #10591046 | semidirect |
| 270. C3 | #10592893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#919 | 2 |
| #11723336 | 2 |
| #11722199 | 2 |
| C3×#63655 | 2 |
| #11722009 | 2 |
| #11722004 | 2 |
| D3×C3⋊(C3⋊C16) | 2 |
| #10592893 | 3 |
| #10591046 | 3 |