Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 106 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. #64078⋊C3 | C2 | semidirect |
| 3. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 5. #63644⋊C3 | C2 | semidirect |
| 6. #10592541 | C3 | semidirect |
| 18. #64078 | C2×C3 | semidirect |
| 22. C32×C4⋊C8 | D3 | semidirect |
| 23. C32×C4⋊C8 | C2×C3 | semidirect |
| 25. #63644 | C2×C3 | semidirect |
| 35. C4⋊((C3⋊D3)⋊C3) | Q8 | semidirect |
| 102. C4⋊(C3⋊D3) | C3×Q8 | semidirect |
| 176. C4⋊C8 | (C3⋊D3)⋊C3 | semidirect |
| 178. H(3,𝔽3) | #476 | semidirect |
| 272. C32 | #4842 | semidirect |
| 273. C32 | C3×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| #64078⋊C3 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #63648⋊C3 | 2 |
| #63644⋊C3 | 2 |
| #10592541 | 3 |
| C3×#4842 | 3 |