Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
298 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #63576 | C2 | direct (N × H) |
| 7. C2×C3⋊(C3⋊C8) | C4 | semidirect |
| 23. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 64. C2×C32 | #107 | semidirect |
| 90. C32 | C2×#107 | semidirect |
| 103. C2×C3 | #807 | semidirect |
| 116. C3 | C2×#807 | semidirect |
| 117. C2 | #63576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C8) | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| #63576 | 2 |
| C2×#807 | 3 |