Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
368 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×#64289 | C2 | semidirect |
| 3. C3×#63785 | C2 | semidirect |
| 4. C3×#63770 | C2 | semidirect |
| 5. C3×#63767 | C2 | semidirect |
| 6. #10593788 | C3 | direct (N × H) |
| 13. C33×Q16 | C4 | semidirect |
| 14. C3×#3755 | C4 | semidirect |
| 15. C3×#3745 | C4 | semidirect |
| 17. #64289 | C2×C3 | semidirect |
| 20. #63785 | C2×C3 | semidirect |
| 21. #63770 | C2×C3 | semidirect |
| 22. #63767 | C2×C3 | semidirect |
| 43. C32×Q16 | C3×C4 | semidirect |
| 44. #3755 | C3×C4 | semidirect |
| 45. #3745 | C3×C4 | semidirect |
| 89. C3×Q16 | #157 | semidirect |
| 119. C33 | #444 | semidirect |
| 147. Q16 | C3×#157 | semidirect |
| 171. C32 | C3×#444 | semidirect |
| 197. C3 | #10593788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64289 | 2 |
| C3×#64128 | 2 |
| C3×#63785 | 2 |
| C3×#63770 | 2 |
| C3×#63767 | 2 |
| #10593788 | 3 |
| C3×#444 | 9 |