Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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×C3×#106 | C2 | semidirect |
| 4. #5106 | C2 | semidirect |
| 5. #4964 | C2 | semidirect |
| 6. #4861 | C2 | semidirect |
| 7. #4860 | C2 | semidirect |
| 8. D3×#106 | C2 | semidirect |
| 16. #901 | C4 | semidirect |
| 37. C2×#106 | D3 | semidirect |
| 47. C2×C3×C8 | C2×C4 | semidirect |
| 59. #208 | C2×C4 | semidirect |
| 61. ΓL(1,𝔽25) | C2×C4 | semidirect |
| 62. D3×C8 | C2×C4 | semidirect |
| 116. C2×C8 | C4×D3 | semidirect |
| 176. C3 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| #5504 | 2 |
| C2×C3×#106 | 2 |
| #5106 | 2 |
| #4964 | 2 |
| #4861 | 2 |
| #4860 | 2 |
| D3×#106 | 2 |
| #2912 | 3 |