Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
279 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×C9×M16 | C2 | semidirect |
| 3. C2×#3667 | C2 | semidirect |
| 4. #63383 | C2 | direct (N × H) |
| 15. C9×M16 | C22 | semidirect |
| 18. #3667 | C22 | semidirect |
| 70. C2×M16 | D9 | semidirect |
| 91. C2×C9 | #100 | semidirect |
| 105. M16 | C2×D9 | semidirect |
| 120. C9 | C2×#100 | semidirect |
| 159. C2 | #63383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D36 | 2 |
| C2×C9×M16 | 2 |
| C2×#3667 | 2 |
| #63383 | 2 |
| C2×#823 | 3 |