Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 48. C4×C9 | Q16 | semidirect |
| 89. C9 | #462 | semidirect |
| 109. C4 | #3674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C9 | 2 |
| C2×#3674 | 2 |
| #63431 | 2 |
| #63368 | 2 |
| C4⋊(C9⋊C8) | 2 |
| #5031 | 3 |