Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2772 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 351 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. #11724679 | C2 | semidirect |
| 2. C33×#120 | C2 | semidirect |
| 3. #11723994 | C2 | semidirect |
| 4. #11722204 | C2 | semidirect |
| 5. #11722176 | C2 | semidirect |
| 7. C24×C33 | C22 | semidirect |
| 17. C33×C22⋊C4 | C22 | semidirect |
| 19. #88864 | C22 | semidirect |
| 21. C32×#120 | D3 | semidirect |
| 28. C23×C33 | D4 | semidirect |
| 31. C22×C3⋊(C3⋊D3) | D4 | semidirect |
| 35. C2×C33×C4 | D4 | semidirect |
| 42. C2×C3⋊(C3⋊Dic3) | D4 | semidirect |
| 47. C24×C32 | C2×D3 | semidirect |
| 57. C32×C22⋊C4 | C2×D3 | semidirect |
| 78. C3×#120 | C3⋊D3 | semidirect |
| 85. C23×C32 | #67 | semidirect |
| 92. C2×C32×C4 | #67 | semidirect |
| 110. C24×C3 | C2×C3⋊D3 | semidirect |
| 120. C3×C22⋊C4 | C2×C3⋊D3 | semidirect |
| 142. #120 | C3⋊(C3⋊D3) | semidirect |
| 145. C33 | B(4,𝔽2) | semidirect |
| 149. C23×C3 | #638 | semidirect |
| 156. C2×C3×C4 | #638 | semidirect |
| 173. C24 | C2×C3⋊(C3⋊D3) | semidirect |
| 185. C22⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 203. C32 | #5032 | semidirect |
| 209. C23 | #6312 | semidirect |
| 224. C2×C4 | #6312 | semidirect |
| 248. C3 | #10592731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724679 | 2 |
| C33×#120 | 2 |
| #11723994 | 2 |
| #11722204 | 2 |
| #11722176 | 2 |
| #10592731 | 3 |