Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
278 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3743 | C2 | semidirect |
| 2. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×C8×Dic3 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. #63557 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 28. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 36. C8×Dic3 | D3 | semidirect |
| 50. C32×C8 | D4 | semidirect |
| 97. C3×Dic3 | M16 | semidirect |
| 137. C3×C8 | D12 | semidirect |
| 138. C3×C8 | #67 | semidirect |
| 194. Dic3 | ΓL(1,𝔽25) | semidirect |
| 195. C32 | #436 | semidirect |
| 211. C8 | #626 | semidirect |
| 240. C3 | #4688 | semidirect |
| 241. C3 | #5128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C4×#626 | 2 |
| C3×C8×Dic3 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63557 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5128 | 3 |
| #4688 | 3 |