Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#3756 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. #63643 | C2 | semidirect |
| 7. #63634 | C2 | semidirect |
| 26. C3×#103 | D3 | semidirect |
| 61. C2×C3⋊D3 | Q16 | semidirect |
| 75. #103 | C3⋊D3 | semidirect |
| 119. C32 | #467 | semidirect |
| 150. C3 | #4813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64155 | 2 |
| C2×#3756 | 2 |
| C2×C8×C3⋊D3 | 2 |
| #64106 | 2 |
| C32×#103 | 2 |
| #63643 | 2 |
| #63634 | 2 |
| #4813 | 3 |