Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 246 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×C3×#3755 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10592784 | C3 | direct (N × H) |
| 15. C32×C4⋊Q8 | D3 | semidirect |
| 16. C32×C4⋊Q8 | C2×C3 | semidirect |
| 17. C2×#3755 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 30. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 54. C33×C4 | SD16 | semidirect |
| 58. C3×C4⋊Q8 | C3×D3 | semidirect |
| 59. C3×C4⋊Q8 | C3⋊D3 | semidirect |
| 83. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 118. C32×C4 | #215 | semidirect |
| 119. C32×C4 | C3×SD16 | semidirect |
| 123. C4⋊Q8 | C3×C3⋊D3 | semidirect |
| 126. C33 | #492 | semidirect |
| 174. C3×C4 | C3×#215 | semidirect |
| 175. C3×C4 | #3755 | semidirect |
| 179. C32 | #5085 | semidirect |
| 180. C32 | C3×#492 | semidirect |
| 201. C4 | C3×#3755 | semidirect |
| 204. C3 | C3×#5085 | semidirect |
| 205. C3 | #10592784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C2×C3×#3755 | 2 |
| C3×#64083 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592784 | 3 |
| C3×#5085 | 3 |