Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
332 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 75 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×#6909 | C2 | semidirect |
| 3. #11757585 | C2 | semidirect |
| 4. C3×C4×#272 | C3 | semidirect |
| 6. C4×#4174 | C3 | semidirect |
| 8. #92281 | C4 | direct (N × H) |
| 12. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 13. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3×#1084 | C2×C3 | semidirect |
| 18. C4×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 19. #66321 | C2×C3 | semidirect |
| 20. #6909 | C2×C4 | semidirect |
| 29. C3×#272 | C3×C4 | semidirect |
| 33. #4174 | C3×C4 | semidirect |
| 39. C33×C4 | C3×D3 | semidirect |
| 57. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 58. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 60. AΣL(1,𝔽27) | C2×C3×C4 | semidirect |
| 111. C33 | C3×C4×D3 | semidirect |
| 185. C4 | #92281 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92281 | 2 |
| C4×#6909 | 2 |
| #11757585 | 2 |
| C3×C4×#272 | 3 |
| C4×D3×H(3,𝔽3) | 3 |
| C4×#4174 | 3 |