Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
387 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×Dic18 | C2 | semidirect |
| 3. #63511 | C2 | direct (N × H) |
| 4. C2×#3674 | C2 | semidirect |
| 5. C2×#3672 | C2 | semidirect |
| 6. C2×#3667 | C2 | semidirect |
| 19. C2×Dic18 | C22 | semidirect |
| 20. #3674 | C22 | semidirect |
| 21. #3672 | C22 | semidirect |
| 22. #3667 | C22 | semidirect |
| 103. C2×C9 | #137 | semidirect |
| 131. C9 | C2×#137 | semidirect |
| 168. C2 | #63511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41 | 2 |
| C22×Dic18 | 2 |
| #63511 | 2 |
| C2×#3674 | 2 |
| C2×#3672 | 2 |
| C2×#3667 | 2 |
| C2×#951 | 3 |