Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
966 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 327 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×#634 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #64133 | C2 | direct (N × H) |
| 6. C2×#3750 | C2 | semidirect |
| 16. C2×#634 | C22 | semidirect |
| 18. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 19. #3750 | C22 | semidirect |
| 28. C23×C32 | Q8 | semidirect |
| 59. C22×C32 | C2×Q8 | semidirect |
| 74. C23×C3 | Dic6 | semidirect |
| 88. C2×C32 | C22⋊Q8 | semidirect |
| 108. C22×C3 | C2×Dic6 | semidirect |
| 116. C32 | C2×C22⋊Q8 | semidirect |
| 119. C23 | #634 | semidirect |
| 133. C2×C3 | #924 | semidirect |
| 141. C22 | C2×#634 | semidirect |
| 149. C3 | C2×#924 | semidirect |
| 151. C2 | #64133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C4 | 2 |
| C22×#634 | 2 |
| C2×#3757 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| #64133 | 2 |
| C2×#3750 | 2 |
| C2×#924 | 3 |