Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
12460 conjugacy classes of subgroups; only the 2491 normal subgroups are shown.
This group has 12460 conjugacy classes of subgroups — too many to draw. Only its 2491 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×#89080 | C2 | direct (N × H) |
| 3. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 4. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 7. C2×C33×Q8 | C22 | semidirect |
| 10. #89080 | C22 | direct (N × H) |
| 11. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 12. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 13. C22×C32×Q8 | D3 | semidirect |
| 20. C33×Q8 | C23 | semidirect |
| 23. C4⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 24. C4×C3⋊(C3⋊D3) | C23 | semidirect |
| 27. C2×C32×Q8 | C2×D3 | semidirect |
| 33. C22×C33 | #41 | semidirect |
| 39. C22×C3×Q8 | C3⋊D3 | semidirect |
| 46. C32×Q8 | C22×D3 | semidirect |
| 52. C2×C33 | C2×#41 | semidirect |
| 56. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 62. C22×C32 | #239 | semidirect |
| 69. C22×Q8 | C3⋊(C3⋊D3) | semidirect |
| 72. C33 | C22×#41 | semidirect |
| 76. C3×Q8 | C22×C3⋊D3 | semidirect |
| 81. C2×C32 | C2×#239 | semidirect |
| 86. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 91. C22×C3 | #3832 | semidirect |
| 97. C32 | C22×#239 | semidirect |
| 101. Q8 | C22×C3⋊(C3⋊D3) | semidirect |
| 106. C2×C3 | C2×#3832 | semidirect |
| 111. C22 | #89080 | direct (N × H) |
| 115. C3 | C22×#3832 | semidirect |
| 117. C2 | C2×#89080 | 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×#89080 | 2 |
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C22×#3832 | 3 |