Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
11900 conjugacy classes of subgroups; only the 2531 normal subgroups are shown.
This group has 11900 conjugacy classes of subgroups — too many to draw. Only its 2531 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. C22×C33×Q8 | C2 | semidirect |
| 2. C2×Q8×C3⋊(C3⋊D3) | C2 | direct (N × H) |
| 4. C22×#6308 | C2 | semidirect |
| 7. C2×C33×Q8 | C22 | semidirect |
| 10. Q8×C3⋊(C3⋊D3) | C22 | direct (N × H) |
| 12. C2×#6308 | C22 | semidirect |
| 13. C22×C32×Q8 | D3 | semidirect |
| 18. C22×C3⋊(C3⋊D3) | Q8 | direct (N × H) |
| 20. C33×Q8 | C23 | semidirect |
| 24. #6308 | C23 | semidirect |
| 27. C2×C32×Q8 | C2×D3 | semidirect |
| 33. C22×C33 | C2×Q8 | semidirect |
| 35. C2×C3⋊(C3⋊D3) | C2×Q8 | direct (N × H) |
| 39. C22×C3×Q8 | C3⋊D3 | semidirect |
| 46. C32×Q8 | C22×D3 | semidirect |
| 52. C2×C33 | C22×Q8 | semidirect |
| 54. C3⋊(C3⋊D3) | C22×Q8 | direct (N × H) |
| 56. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 62. C22×C32 | D3×Q8 | semidirect |
| 70. C22×Q8 | C3⋊(C3⋊D3) | direct (N × H) |
| 72. C33 | C23×Q8 | semidirect |
| 76. C3×Q8 | C22×C3⋊D3 | semidirect |
| 81. C2×C32 | C2×D3×Q8 | semidirect |
| 87. C2×Q8 | C2×C3⋊(C3⋊D3) | direct (N × H) |
| 91. C22×C3 | Q8×C3⋊D3 | semidirect |
| 97. C32 | C22×D3×Q8 | semidirect |
| 102. Q8 | C22×C3⋊(C3⋊D3) | direct (N × H) |
| 106. C2×C3 | C2×Q8×C3⋊D3 | semidirect |
| 111. C22 | Q8×C3⋊(C3⋊D3) | direct (N × H) |
| 115. C3 | C22×Q8×C3⋊D3 | semidirect |
| 117. C2 | C2×Q8×C3⋊(C3⋊D3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C22×#6308 | 2 |
| C22×Q8×C3⋊D3 | 3 |