Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
614 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 111 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. C3×#64078 | C2 | semidirect |
| 3. C3×#63630 | C2 | semidirect |
| 4. #11722076 | C2 | semidirect |
| 19. #64078 | D3 | semidirect |
| 26. #63630 | D3 | semidirect |
| 261. C33 | #489 | semidirect |
| 397. C32 | #4714 | semidirect |
| 398. C32 | #5055 | semidirect |
| 399. C32 | #5089 | semidirect |
| 448. C3 | #10590276 | semidirect |
| 449. C3 | #10590280 | semidirect |
| 450. C3 | #10590294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64084 | 2 |
| C3×#64078 | 2 |
| C3×#63630 | 2 |
| #11722076 | 2 |
| #11722075 | 2 |
| #10590294 | 3 |
| #10590280 | 3 |
| #10590276 | 3 |