Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 43 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. Q8×C22⋊C9 | C2 | semidirect |
| 3. (C22⋊C9)⋊Q8 | C2 | semidirect |
| 17. (C22⋊C9)⋊C2 | Q8 | direct (N × H) |
| 37. C22⋊C9 | C2×Q8 | semidirect |
| 41. C22×Q8 | D9 | semidirect |
| 97. Q8 | (C22⋊C9)⋊C2 | direct (N × H) |
| 116. C22 | Q8×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊C9 | 2 |
| C4×(C22⋊C9)⋊C2 | 2 |
| (C22⋊C9)⋊Q8 | 2 |
| Q8×#67 | 3 |
| Q8×D9 | 4 |