Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
109 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 109 conjugacy classes of subgroups — too many to draw. Only its 31 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 |
|---|---|---|
| 74. C32 | #479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#157 | 2 |
| #64243 | 2 |
| #63784 | 2 |
| #63746 | 2 |
| #63745 | 2 |
| #63744 | 2 |
| #479 | 9 |