Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
660 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×Q8×D27 | C2 | semidirect |
| 3. C27×#124 | C2 | semidirect |
| 4. #11720196 | C2 | semidirect |
| 5. #11720185 | C2 | semidirect |
| 6. #11720134 | C2 | semidirect |
| 7. C22⋊C4×D27 | C2 | semidirect |
| 8. #11720124 | C2 | semidirect |
| 9. C42×D27 | C2 | semidirect |
| 12. C2×Q8×C27 | C22 | semidirect |
| 21. C2×Dic54 | C22 | semidirect |
| 22. C2×Dic54 | C22 | semidirect |
| 23. C22⋊C4×C27 | C22 | semidirect |
| 24. C42×C27 | C22 | semidirect |
| 25. #88372 | C22 | semidirect |
| 26. (C2×D27)⋊C4 | C22 | semidirect |
| 27. (C2×D27)⋊C4 | C22 | semidirect |
| 28. C4×Dic27 | C22 | semidirect |
| 29. C4×Dic27 | C22 | semidirect |
| 127. D27 | #124 | direct (N × H) |
| 167. #124 | D27 | direct (N × H) |
| 170. C27 | C2×#124 | semidirect |
| 200. C2×Q8 | C2×D27 | semidirect |
| 211. C22⋊C4 | C2×D27 | semidirect |
| 214. C42 | C2×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D27 | 2 |
| C2×D4×D27 | 2 |
| C27×#124 | 2 |
| #11720196 | 2 |
| #11720185 | 2 |
| #11720134 | 2 |
| C22⋊C4×D27 | 2 |
| #11720124 | 2 |
| C42×D27 | 2 |
| D9×#124 | 3 |