Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 306 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. C33×C4⋊Q8 | C2 | semidirect |
| 2. C2×C32×#215 | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 6. C3×#5085 | C3 | direct (N × H) |
| 16. C32×C4⋊Q8 | D3 | semidirect |
| 17. C32×C4⋊Q8 | C2×C3 | semidirect |
| 19. C2×C3×#215 | C2×C3 | semidirect |
| 22. C3×C4×C3⋊C8 | C2×C3 | semidirect |
| 30. C32×C3⋊C8 | D4 | semidirect |
| 32. #5085 | C32 | direct (N × H) |
| 54. C33×C4 | SD16 | semidirect |
| 58. C3×C4⋊Q8 | C3×D3 | semidirect |
| 59. C3×C4⋊Q8 | C2×C32 | semidirect |
| 61. C2×#215 | C2×C32 | semidirect |
| 64. C4×C3⋊C8 | C2×C32 | semidirect |
| 84. C3×C3⋊C8 | C3×D4 | semidirect |
| 118. C32×C4 | #215 | semidirect |
| 119. C32×C4 | C3×SD16 | semidirect |
| 123. C4⋊Q8 | C32×D3 | semidirect |
| 126. C33 | #492 | semidirect |
| 146. C3⋊C8 | C32×D4 | semidirect |
| 174. C3×C4 | C3×#215 | semidirect |
| 175. C3×C4 | C32×SD16 | semidirect |
| 179. C32 | #5085 | direct (N × H) |
| 180. C32 | C3×#492 | semidirect |
| 201. C4 | C32×#215 | semidirect |
| 204. C3 | C3×#5085 | direct (N × H) |
| 205. C3 | C32×#492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C2×C32×#215 | 2 |
| C32×#874 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#492 | 3 |
| C3×#5085 | 3 |