Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 132 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. C4⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 4. #63630⋊C3 | C2 | semidirect |
| 5. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 6. #10592699 | C3 | semidirect |
| 19. C4⋊(C3⋊(C3⋊C8)) | C2×C3 | semidirect |
| 20. #63630 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 157. H(3,𝔽3) | #433 | semidirect |
| 233. C32 | #5000 | semidirect |
| 234. C32 | C3×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#117 | 2 |
| #63657⋊C3 | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #63630⋊C3 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #10592699 | 3 |
| C3×#5000 | 3 |