Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
374 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 3. C2×#3719 | C2 | semidirect |
| 5. #63567 | C2 | semidirect |
| 73. C22×C32 | Q16 | semidirect |
| 143. C22×C3 | Dic12 | semidirect |
| 144. C22×C3 | #216 | semidirect |
| 160. C32 | #451 | semidirect |
| 188. C22 | #3719 | semidirect |
| 196. C3 | #4739 | semidirect |
| 197. C3 | #5050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C3×#924 | 2 |
| C2×#3719 | 2 |
| C3×#830 | 2 |
| #63567 | 2 |
| #5050 | 3 |
| #4739 | 3 |