Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
334 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 70 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. M16×C3⋊D3 | C2 | semidirect |
| 3. #63818 | C2 | semidirect |
| 4. C3×#824 | C2 | semidirect |
| 5. C3×#823 | C2 | semidirect |
| 6. #63560 | C2 | semidirect |
| 7. #63558 | C2 | semidirect |
| 39. #824 | D3 | semidirect |
| 41. #823 | D3 | semidirect |
| 224. C32 | #413 | semidirect |
| 272. C3 | #4745 | semidirect |
| 273. C3 | #4751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3796 | 2 |
| M16×C3⋊D3 | 2 |
| #63818 | 2 |
| C3×#824 | 2 |
| C3×#823 | 2 |
| #63560 | 2 |
| #63558 | 2 |
| #4751 | 3 |
| #4745 | 3 |