Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
1014 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1014 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×D4 | C2 | semidirect |
| 2. C22×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×#3753 | C2 | direct (N × H) |
| 4. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 9. C2×C32×D4 | C22 | semidirect |
| 12. C2×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. #3753 | C22 | direct (N × H) |
| 14. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. C22×C3×D4 | D3 | semidirect |
| 25. C32×D4 | C23 | semidirect |
| 29. C4⋊(C3⋊D3) | C23 | semidirect |
| 30. C3⋊(C3⋊C8) | C23 | semidirect |
| 35. C2×C3×D4 | C2×D3 | semidirect |
| 43. C22×C32 | D8 | semidirect |
| 50. C22×D4 | C3⋊D3 | semidirect |
| 59. C3×D4 | C22×D3 | semidirect |
| 66. C2×C32 | C2×D8 | semidirect |
| 74. C2×D4 | C2×C3⋊D3 | semidirect |
| 80. C22×C3 | #213 | semidirect |
| 86. C32 | C22×D8 | semidirect |
| 95. D4 | C22×C3⋊D3 | semidirect |
| 100. C2×C3 | C2×#213 | semidirect |
| 107. C22 | #3753 | direct (N × H) |
| 111. C3 | C22×#213 | semidirect |
| 114. C2 | C2×#3753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C22×C4⋊(C3⋊D3) | 2 |
| C2×#3753 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| C22×#213 | 3 |