Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
467 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 467 conjugacy classes of subgroups — too many to draw. Only its 112 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. C4×D4×3−1+2 | C2 | semidirect |
| 2. C2×#3673⋊C3 | C2 | semidirect |
| 3. #11721394 | C2 | semidirect |
| 4. #63369⋊C3 | C2 | semidirect |
| 5. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 7. #10588698 | C3 | semidirect |
| 24. C4×D4×C9 | C2×C3 | semidirect |
| 25. C2×#3673 | C2×C3 | semidirect |
| 26. #63436 | C2×C3 | semidirect |
| 27. #63369 | C2×C3 | semidirect |
| 28. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 32. D4×3−1+2 | D4 | semidirect |
| 79. C4×3−1+2 | D8 | semidirect |
| 112. D4×C9 | C3×D4 | semidirect |
| 184. C4×C9 | C3×D8 | semidirect |
| 189. C4×D4 | AGL(1,ℤ/9) | semidirect |
| 192. 3−1+2 | #459 | semidirect |
| 271. C9 | C3×#459 | semidirect |
| 279. D4 | C4⋊AGL(1,ℤ/9) | semidirect |
| 305. C4 | #3673⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×3−1+2 | 2 |
| C2×#3673⋊C3 | 2 |
| #11721394 | 2 |
| #63369⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5015 | 3 |
| #10588698 | 3 |