Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 95 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. H(3,𝔽3)×#135 | C2 | semidirect |
| 2. C2×#88529 | C2 | semidirect |
| 3. #11720569 | C2 | semidirect |
| 4. #11720565 | C2 | semidirect |
| 5. #11720545 | C2 | semidirect |
| 9. Q16×H(3,𝔽3) | C22 | semidirect |
| 11. D8×H(3,𝔽3) | C22 | semidirect |
| 15. #88386 | C22 | semidirect |
| 16. C32×#135 | D3 | semidirect |
| 35. C32×Q16 | C2×D3 | semidirect |
| 37. C32×D8 | C2×D3 | semidirect |
| 99. #135 | #272 | semidirect |
| 104. H(3,𝔽3) | #509 | semidirect |
| 131. Q16 | C2×#272 | semidirect |
| 135. D8 | C2×#272 | semidirect |
| 152. C32 | #5193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#135 | 2 |
| C2×#88529 | 2 |
| #11720569 | 2 |
| #11720565 | 2 |
| #11720545 | 2 |
| C3×#5193 | 3 |