Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C2×#3748 | C2 | semidirect |
| 3. C2×D3×C3⋊C8 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 32. #830 | D3 | semidirect |
| 51. C3⋊(C3⋊C8) | D4 | semidirect |
| 91. C2×C3×D3 | M16 | semidirect |
| 179. C2×D3 | #208 | semidirect |
| 195. C32 | #435 | semidirect |
| 240. C3 | #4728 | semidirect |
| 241. C3 | #5011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3748 | 2 |
| C3×C4×#67 | 2 |
| C2×D3×C3⋊C8 | 2 |
| C3×#830 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #63554 | 2 |
| #5011 | 3 |
| #4728 | 3 |