Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
288 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 29. #634 | Q8 | semidirect |
| 84. C32 | #477 | semidirect |
| 106. C3 | #4850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64078 | 2 |
| C4×#634 | 2 |
| C32×C4⋊C8 | 2 |
| #63645 | 2 |
| #63643 | 2 |
| #4850 | 3 |