Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
938 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 168 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. C32×#874 | C2 | semidirect |
| 2. C2×C3×#3713 | C2 | semidirect |
| 3. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10590352 | C3 | direct (N × H) |
| 14. C3×#874 | D3 | semidirect |
| 15. C3×#874 | C2×C3 | semidirect |
| 16. C2×#3713 | C2×C3 | semidirect |
| 17. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 25. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 49. C33×C4 | D8 | semidirect |
| 56. #874 | C3×D3 | semidirect |
| 82. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 126. C32×C4 | #213 | semidirect |
| 127. C32×C4 | C3×D8 | semidirect |
| 133. C33 | #493 | semidirect |
| 197. C3×C4 | #3713 | semidirect |
| 198. C3×C4 | C3×#213 | semidirect |
| 204. C32 | #5073 | semidirect |
| 205. C32 | C3×#493 | semidirect |
| 229. C4 | C3×#3713 | semidirect |
| 234. C3 | #10590352 | direct (N × H) |
| 235. C3 | C3×#5073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#874 | 2 |
| C2×C3×#3713 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C3×#5073 | 3 |
| #10590352 | 3 |