Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 118 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×C3×C9×C4⋊C4 | C2 | semidirect |
| 3. C3×#63389 | C2 | semidirect |
| 4. C3×#63369 | C2 | semidirect |
| 5. C3×#63367 | C2 | semidirect |
| 7. #10588651 | C3 | direct (N × H) |
| 23. C2×C9×C4⋊C4 | C2×C3 | semidirect |
| 25. #63389 | C2×C3 | semidirect |
| 26. #63369 | C2×C3 | semidirect |
| 27. #63367 | C2×C3 | semidirect |
| 76. C2×C3×C4⋊C4 | D9 | semidirect |
| 171. C2×C4⋊C4 | C3×D9 | semidirect |
| 175. C3×C9 | #481 | semidirect |
| 258. C9 | C3×#481 | semidirect |
| 296. C3 | #10588651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C4⋊C4 | 2 |
| C3×#63492 | 2 |
| C3×#63389 | 2 |
| C3×#63369 | 2 |
| C3×#63367 | 2 |
| C3×#4968 | 3 |
| #10588651 | 3 |