Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1518 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 327 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. C3×Q8×C3⋊Dic3 | C2 | semidirect |
| 3. #11723691 | C2 | semidirect |
| 4. #11723689 | C2 | semidirect |
| 5. #11723673 | C2 | semidirect |
| 9. C3×#3832 | C4 | semidirect |
| 21. Q8×C3⋊Dic3 | D3 | semidirect |
| 33. C33×Q8 | C2×C4 | semidirect |
| 38. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 39. C3×C4×C3⋊D3 | C2×C4 | semidirect |
| 48. #3832 | Dic3 | semidirect |
| 102. C32×Q8 | C4×D3 | semidirect |
| 103. C32×Q8 | C2×Dic3 | semidirect |
| 112. C4⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 113. C4×C3⋊D3 | C2×Dic3 | semidirect |
| 199. C33 | #520 | semidirect |
| 206. C3×Q8 | D3×Dic3 | semidirect |
| 207. C3×Q8 | #624 | semidirect |
| 293. C32 | #5574 | semidirect |
| 294. C32 | #5827 | semidirect |
| 296. Q8 | #6294 | semidirect |
| 333. C3 | #10595353 | semidirect |
| 334. C3 | #10595394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3832 | 2 |
| C3×Q8×C3⋊Dic3 | 2 |
| #11723691 | 2 |
| #11723689 | 2 |
| #11723673 | 2 |
| #10595394 | 3 |
| #10595353 | 3 |