Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
243 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 243 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 |
|---|---|---|
| 4. #63376 | C2 | direct (N × H) |
| 11. C2×Dic18 | C4 | semidirect |
| 32. Dic18 | C2×C4 | semidirect |
| 72. C2×C9 | #103 | semidirect |
| 96. C9 | C2×#103 | semidirect |
| 124. C2 | #63376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic18 | 2 |
| C22×C8×C9 | 2 |
| C2×C4⋊Dic9 | 2 |
| #63376 | 2 |
| C2×#816 | 3 |