Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
689 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C3×AΣL(1,𝔽27) | C2 | semidirect |
| 2. C2×C3×#4174 | C2 | semidirect |
| 3. C3×#66321 | C2 | semidirect |
| 5. C3×#6235 | C3 | semidirect |
| 6. #10619641 | C3 | direct (N × H) |
| 10. C22×C34 | D3 | semidirect |
| 14. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 15. C2×C3×#272 | C2×C3 | semidirect |
| 16. C3×#1084 | C2×C3 | semidirect |
| 18. C22×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 19. C2×#4174 | C2×C3 | semidirect |
| 20. #66321 | C2×C3 | semidirect |
| 21. C3×AΣL(1,𝔽27) | D4 | semidirect |
| 27. #6235 | C32 | semidirect |
| 47. C22×C33 | C3×D3 | semidirect |
| 61. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 63. C2×#272 | C2×C32 | semidirect |
| 64. #1084 | C2×C32 | semidirect |
| 65. C34 | #67 | semidirect |
| 67. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 69. AΣL(1,𝔽27) | C3×D4 | semidirect |
| 141. C33 | C3×#67 | semidirect |
| 146. H(3,𝔽3) | C32×D4 | semidirect |
| 193. C22×C3 | #4174 | semidirect |
| 235. C22 | C3×#4174 | semidirect |
| 242. C3 | #10619641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×AΣL(1,𝔽27) | 2 |
| C2×C3×#4174 | 2 |
| C3×#66321 | 2 |
| C33×#67 | 3 |
| C3×#6235 | 3 |
| #10619641 | 3 |