Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 114 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×#63469 | C2 | semidirect |
| 3. C3×C9×#108 | C2 | semidirect |
| 4. C3×#63384 | C2 | semidirect |
| 5. C3×#63375 | C2 | semidirect |
| 7. #10588574 | C3 | direct (N × H) |
| 13. C3×D72 | C4 | semidirect |
| 14. C3×#3664 | C4 | semidirect |
| 17. C3×Dic36 | C4 | semidirect |
| 23. #63469 | C2×C3 | semidirect |
| 26. C9×#108 | C2×C3 | semidirect |
| 27. #63384 | C2×C3 | semidirect |
| 28. #63375 | C2×C3 | semidirect |
| 58. D72 | C3×C4 | semidirect |
| 59. #3664 | C3×C4 | semidirect |
| 62. Dic36 | C3×C4 | semidirect |
| 74. C3×#108 | D9 | semidirect |
| 147. #108 | C3×D9 | semidirect |
| 150. C3×C9 | #444 | semidirect |
| 210. C9 | C3×#444 | semidirect |
| 236. C3 | #10588574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63469 | 2 |
| C3×#63467 | 2 |
| C3×C9×#108 | 2 |
| C3×#63384 | 2 |
| C3×#63375 | 2 |
| C3×#4894 | 3 |
| #10588574 | 3 |