Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
287 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 88 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×C3×D3×C8 | C2 | semidirect |
| 3. C2×D3×C3⋊C8 | C2 | semidirect |
| 4. #63641 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. #63553 | C2 | semidirect |
| 28. C2×D3×C8 | D3 | semidirect |
| 32. (C2×D3)⋊C8 | D3 | semidirect |
| 49. #625 | C8 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 89. C2×C3×D3 | C2×C8 | semidirect |
| 90. C2×C3×D3 | C2×C8 | semidirect |
| 94. C3⋊Dic3 | C2×C8 | semidirect |
| 140. C3⋊C8 | #67 | semidirect |
| 172. C2×D3 | D3×C8 | semidirect |
| 173. C2×D3 | D3×C8 | semidirect |
| 190. C32 | C8×D4 | semidirect |
| 234. C3 | #67⋊C8 | semidirect |
| 235. C3 | C8×#67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C8 | 2 |
| C4×#625 | 2 |
| C2×D3×C3⋊C8 | 2 |
| #63641 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #63553 | 2 |
| C8×#67 | 3 |
| #67⋊C8 | 3 |