Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 631 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 631 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 |
|---|---|---|
| 2. D4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. #11722202 | C2 | semidirect |
| 4. #11722188 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 9. C33×D8 | C4 | semidirect |
| 22. C33×D4 | C2×C4 | semidirect |
| 28. C33×C8 | C2×C4 | semidirect |
| 33. C32×D8 | Dic3 | semidirect |
| 47. C3⋊(C3⋊Dic3) | D8 | direct (N × H) |
| 55. C32×D4 | C2×Dic3 | semidirect |
| 61. C32×C8 | C2×Dic3 | semidirect |
| 70. C3×D8 | C3⋊Dic3 | semidirect |
| 90. C33 | C4×D8 | semidirect |
| 93. C3×D4 | C2×C3⋊Dic3 | semidirect |
| 99. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 107. D8 | C3⋊(C3⋊Dic3) | direct (N × H) |
| 122. C32 | Dic3×D8 | semidirect |
| 125. D4 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 132. C8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 146. C3 | D8×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| #11722202 | 2 |
| #11722188 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| D8×C3⋊Dic3 | 3 |