Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
255 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 255 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×C42×C9 | C2 | semidirect |
| 3. C2×#3667 | C2 | semidirect |
| 4. #63364 | C2 | direct (N × H) |
| 11. #3697 | C4 | semidirect |
| 13. C2×D36 | C4 | semidirect |
| 15. C2×Dic18 | C4 | semidirect |
| 17. C42×C9 | C22 | semidirect |
| 19. #3667 | C22 | semidirect |
| 39. D36 | C2×C4 | semidirect |
| 43. Dic18 | C2×C4 | semidirect |
| 75. C2×C42 | D9 | semidirect |
| 99. C2×C9 | #104 | semidirect |
| 116. C42 | C2×D9 | semidirect |
| 129. C9 | C2×#104 | semidirect |
| 171. C2 | #63364 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3697 | 2 |
| C2×C42×C9 | 2 |
| C2×#3667 | 2 |
| #63364 | 2 |
| C2×#805 | 3 |