Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C2×#3746 | C2 | semidirect |
| 4. #63645 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 44. C22×C32 | Q16 | semidirect |
| 82. C22×C3 | Dic12 | semidirect |
| 89. C32 | #467 | semidirect |
| 107. C22 | #3746 | semidirect |
| 114. C3 | #5116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C8 | 2 |
| #64133 | 2 |
| C2×#3746 | 2 |
| #63645 | 2 |
| #63643 | 2 |
| #5116 | 3 |