Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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×#3743 | C2 | semidirect |
| 2. C2×C8×C3⋊D3 | C2 | semidirect |
| 4. C32×C4⋊C8 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. #63647 | C2 | semidirect |
| 7. #63630 | C2 | semidirect |
| 25. C3×C4⋊C8 | D3 | semidirect |
| 44. C3⋊(C3⋊C8) | D4 | semidirect |
| 65. C2×C3⋊D3 | M16 | semidirect |
| 75. C4⋊C8 | C3⋊D3 | semidirect |
| 126. C32 | #435 | semidirect |
| 161. C3 | #4836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| C32×C4⋊C8 | 2 |
| #63647 | 2 |
| #63630 | 2 |
| #4836 | 3 |