Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
593 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 593 conjugacy classes of subgroups — too many to draw. Only its 77 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. M16×#272 | C2 | semidirect |
| 3. #11721065 | C2 | semidirect |
| 4. #63650⋊C3 | C2 | semidirect |
| 5. #63651⋊C3 | C2 | semidirect |
| 6. #11720321 | C2 | semidirect |
| 7. #11720320 | C2 | semidirect |
| 34. #63651 | D3 | semidirect |
| 35. #63650 | D3 | semidirect |
| 288. H(3,𝔽3) | #413 | semidirect |
| 434. C32 | #4745 | semidirect |
| 435. C32 | #4751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88649 | 2 |
| M16×#272 | 2 |
| #11721065 | 2 |
| #63650⋊C3 | 2 |
| #63651⋊C3 | 2 |
| #11720321 | 2 |
| #11720320 | 2 |
| #10591007 | 3 |
| #10591006 | 3 |