Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#3718 | C2 | semidirect |
| 4. #63576 | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 55. C22×C32 | Q16 | semidirect |
| 108. C22×C3 | #216 | semidirect |
| 120. C32 | #467 | semidirect |
| 142. C22 | #3718 | semidirect |
| 150. C3 | #5051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C8) | 2 |
| C3×#924 | 2 |
| C2×#3718 | 2 |
| #63576 | 2 |
| #63565 | 2 |
| #5051 | 3 |