Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3744 | C2 | semidirect |
| 2. C2×#3743 | C2 | semidirect |
| 3. #64106 | C2 | semidirect |
| 5. C32×#107 | C2 | semidirect |
| 6. #63637 | C2 | semidirect |
| 7. #63636 | C2 | semidirect |
| 26. C3×#107 | D3 | semidirect |
| 43. C32×C8 | D4 | semidirect |
| 76. #107 | C3⋊D3 | semidirect |
| 93. C3×C8 | D12 | semidirect |
| 126. C32 | #468 | semidirect |
| 142. C8 | C4⋊(C3⋊D3) | semidirect |
| 161. C3 | #4886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| C2×#3743 | 2 |
| #64106 | 2 |
| #64104 | 2 |
| C32×#107 | 2 |
| #63637 | 2 |
| #63636 | 2 |
| #4886 | 3 |