Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
1064 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 319 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. C2×C33×D4 | C2 | semidirect |
| 2. C2×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 3. #88860 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 9. C33×D4 | C22 | semidirect |
| 12. C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 13. C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 14. C2×C32×D4 | D3 | semidirect |
| 29. C32×D4 | C2×D3 | semidirect |
| 35. C2×C33 | D8 | semidirect |
| 38. C2×C3×D4 | C3⋊D3 | semidirect |
| 50. C33 | C2×D8 | semidirect |
| 54. C3×D4 | C2×C3⋊D3 | semidirect |
| 60. C2×C32 | #213 | semidirect |
| 64. C2×D4 | C3⋊(C3⋊D3) | semidirect |
| 74. C32 | C2×#213 | semidirect |
| 80. D4 | C2×C3⋊(C3⋊D3) | semidirect |
| 84. C2×C3 | #3753 | semidirect |
| 94. C3 | C2×#3753 | semidirect |
| 97. C2 | #88860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #88860 | 2 |
| C2×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C2×#3753 | 3 |