Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 96 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. #63498⋊C3 | C2 | semidirect |
| 3. D4×3−1+2⋊C4 | C2 | semidirect |
| 4. C2×#3672⋊C3 | C2 | semidirect |
| 5. #63392⋊C3 | C2 | semidirect |
| 6. #63376⋊C3 | C2 | semidirect |
| 7. (3−1+2⋊C4)⋊C8 | C2 | semidirect |
| 9. #10588833 | C3 | semidirect |
| 32. #63498 | C2×C3 | semidirect |
| 33. D4×Dic9 | C2×C3 | semidirect |
| 34. C2×#3672 | C2×C3 | semidirect |
| 35. #63392 | C2×C3 | semidirect |
| 36. #63376 | C2×C3 | semidirect |
| 37. Dic9⋊C8 | C2×C3 | semidirect |
| 227. 3−1+2 | #463 | semidirect |
| 316. C9 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×3−1+2 | 2 |
| #63498⋊C3 | 2 |
| D4×3−1+2⋊C4 | 2 |
| C2×#3672⋊C3 | 2 |
| #63392⋊C3 | 2 |
| #63376⋊C3 | 2 |
| (3−1+2⋊C4)⋊C8 | 2 |
| C3×#5153 | 3 |
| #10588833 | 3 |