Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
295 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×#924 | C2 | semidirect |
| 3. C22×C3×C3⋊C8 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. #63573 | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 7. #63564 | C2 | semidirect |
| 29. #924 | D3 | semidirect |
| 30. C22×C3⋊C8 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 88. C22×C32 | SD16 | semidirect |
| 147. C3⋊C8 | #67 | semidirect |
| 174. C22×C3 | #204 | semidirect |
| 175. C22×C3 | #215 | semidirect |
| 203. C32 | #465 | semidirect |
| 240. C22 | #3717 | semidirect |
| 249. C3 | #5048 | semidirect |
| 250. C3 | #5114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| C3×#924 | 2 |
| C22×C3×C3⋊C8 | 2 |
| C2×#3717 | 2 |
| #63573 | 2 |
| #63566 | 2 |
| #63564 | 2 |
| #5114 | 3 |
| #5048 | 3 |