Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1764 conjugacy classes of subgroups; only the 477 normal subgroups are shown.
This group has 1764 conjugacy classes of subgroups — too many to draw. Only its 477 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 |
|---|---|---|
| 3. C33×C4⋊C8 | C2 | semidirect |
| 4. #11722184 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 19. C32×C4⋊C8 | D3 | semidirect |
| 51. C33×C4 | M16 | semidirect |
| 56. C3⋊(C3⋊Dic3) | M16 | semidirect |
| 59. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 95. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 105. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 106. C33 | #423 | semidirect |
| 139. C3×C4 | #3743 | semidirect |
| 145. C32 | #4837 | semidirect |
| 171. C4 | #88850 | semidirect |
| 174. C3 | #10592536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88850 | 2 |
| C42×C3⋊(C3⋊D3) | 2 |
| C33×C4⋊C8 | 2 |
| #11722184 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592536 | 3 |