Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3107 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 3107 conjugacy classes of subgroups — too many to draw. Only its 299 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. C22×#6199 | C2 | semidirect |
| 3. C2×#3757⋊C3 | C2 | semidirect |
| 4. #11721320 | C2 | direct (N × H) |
| 5. C2×#88451 | C2 | semidirect |
| 9. C23×#272 | C4 | semidirect |
| 13. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 15. C2×#6199 | C22 | semidirect |
| 16. #3757⋊C3 | C22 | semidirect |
| 17. #88451 | C22 | semidirect |
| 21. C2×#3757 | D3 | semidirect |
| 26. C23×H(3,𝔽3) | C2×C4 | semidirect |
| 33. C22×#272 | C2×C4 | semidirect |
| 34. C22×#272 | C2×C4 | semidirect |
| 39. C2×(C3⋊Dic3)⋊C3 | C23 | semidirect |
| 55. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 59. #3757 | C2×D3 | semidirect |
| 65. C22×H(3,𝔽3) | C22×C4 | semidirect |
| 71. C2×#272 | C22⋊C4 | semidirect |
| 73. C2×#272 | C22×C4 | semidirect |
| 93. C23×C32 | C4×D3 | semidirect |
| 115. C2×C3⋊Dic3 | C22×D3 | semidirect |
| 121. C2×H(3,𝔽3) | C2×C22⋊C4 | semidirect |
| 125. #272 | C2×C22⋊C4 | semidirect |
| 165. C22×C32 | C2×C4×D3 | semidirect |
| 189. H(3,𝔽3) | C22×C22⋊C4 | semidirect |
| 242. C2×C32 | D3×C22⋊C4 | semidirect |
| 303. C32 | C2×D3×C22⋊C4 | semidirect |
| 314. C23 | #6199 | semidirect |
| 348. C22 | C2×#6199 | semidirect |
| 358. C2 | #11721320 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#272 | 2 |
| C22×#6199 | 2 |
| C2×#3757⋊C3 | 2 |
| #11721320 | 2 |
| C2×#88451 | 2 |
| C2×D3×#217 | 3 |