Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
894 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 279 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×C32×Q8 | C2 | semidirect |
| 3. C2×#3755 | C2 | direct (N × H) |
| 4. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 8. C2×C32×Q8 | C22 | semidirect |
| 13. #3755 | C22 | direct (N × H) |
| 14. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. C22×C3×Q8 | D3 | semidirect |
| 23. C32×Q8 | C23 | semidirect |
| 29. C3⋊(C3⋊C8) | C23 | semidirect |
| 33. C2×C3×Q8 | C2×D3 | semidirect |
| 40. C22×C32 | SD16 | semidirect |
| 47. C22×Q8 | C3⋊D3 | semidirect |
| 55. C3×Q8 | C22×D3 | semidirect |
| 62. C2×C32 | C2×SD16 | semidirect |
| 67. C2×Q8 | C2×C3⋊D3 | semidirect |
| 74. C22×C3 | #215 | semidirect |
| 81. C32 | C22×SD16 | semidirect |
| 86. Q8 | C22×C3⋊D3 | semidirect |
| 93. C2×C3 | C2×#215 | semidirect |
| 98. C22 | #3755 | direct (N × H) |
| 103. C3 | C22×#215 | semidirect |
| 105. C2 | C2×#3755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C22×C4⋊(C3⋊D3) | 2 |
| C2×#3755 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| C22×#215 | 3 |