Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
419 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 419 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×Q8×3−1+2 | C2 | semidirect |
| 2. C2×#3675⋊C3 | C2 | semidirect |
| 4. #63369⋊C3 | C2 | semidirect |
| 5. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 7. #10588710 | C3 | semidirect |
| 24. C4×Q8×C9 | C2×C3 | semidirect |
| 25. C2×#3675 | C2×C3 | semidirect |
| 27. #63369 | C2×C3 | semidirect |
| 28. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 31. Q8×3−1+2 | D4 | semidirect |
| 76. C4×3−1+2 | SD16 | semidirect |
| 106. Q8×C9 | C3×D4 | semidirect |
| 171. C4×C9 | C3×SD16 | semidirect |
| 176. C4×Q8 | AGL(1,ℤ/9) | semidirect |
| 179. 3−1+2 | #460 | semidirect |
| 249. C9 | C3×#460 | semidirect |
| 252. Q8 | C4⋊AGL(1,ℤ/9) | semidirect |
| 278. C4 | #3675⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×3−1+2 | 2 |
| C2×#3675⋊C3 | 2 |
| #11721394 | 2 |
| #63369⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5027 | 3 |
| #10588710 | 3 |