Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1092 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. #11723992 | C2 | semidirect |
| 3. #11723455 | C2 | semidirect |
| 4. #11723379 | C2 | semidirect |
| 5. C3×#63664 | C2 | semidirect |
| 6. #11722044 | C2 | semidirect |
| 7. #11722028 | C2 | semidirect |
| 37. #63664 | D3 | semidirect |
| 260. C33 | #456 | semidirect |
| 369. C32 | #4826 | semidirect |
| 370. C32 | #5246 | semidirect |
| 415. C3 | #10591689 | semidirect |
| 416. C3 | #10592945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1010 | 2 |
| #11723992 | 2 |
| #11723455 | 2 |
| #11723379 | 2 |
| C3×#63664 | 2 |
| #11722044 | 2 |
| #11722028 | 2 |
| #10592945 | 3 |
| #10591689 | 3 |