Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 351 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. C4⋊C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×#102 | C2 | semidirect |
| 4. #11722202 | C2 | semidirect |
| 5. #11722190 | C2 | semidirect |
| 6. #11722188 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 22. C32×#102 | D3 | semidirect |
| 69. C3×#102 | C3⋊D3 | semidirect |
| 124. #102 | C3⋊(C3⋊D3) | semidirect |
| 126. C33 | #480 | semidirect |
| 171. C32 | #4774 | semidirect |
| 205. C3 | #10592473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723979 | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C33×#102 | 2 |
| #11722202 | 2 |
| #11722190 | 2 |
| #11722188 | 2 |
| #11722177 | 2 |
| #10592473 | 3 |