Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 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×H(5,𝔽2) | C2 | semidirect |
| 2. C2×#937 | C2 | semidirect |
| 3. #5244 | C2 | direct (N × H) |
| 4. C2×#834 | C2 | semidirect |
| 6. C24×D3 | C22 | semidirect |
| 8. C3×H(5,𝔽2) | C22 | semidirect |
| 13. C2×#217 | C22 | semidirect |
| 15. #937 | C22 | semidirect |
| 17. #834 | C22 | semidirect |
| 18. C2×H(5,𝔽2) | D3 | semidirect |
| 23. C24×C3 | D4 | semidirect |
| 28. C23×D3 | C23 | semidirect |
| 37. C2×C3×D4 | D4 | semidirect |
| 40. C22×C3×C4 | D4 | semidirect |
| 45. #217 | C23 | semidirect |
| 49. H(5,𝔽2) | C2×D3 | semidirect |
| 67. C23×C3 | C2×D4 | semidirect |
| 83. C2×C3×C4 | C2×D4 | semidirect |
| 92. C24 | #67 | semidirect |
| 104. C2×D4 | #67 | semidirect |
| 108. C22×C4 | #67 | semidirect |
| 145. C23 | C2×#67 | semidirect |
| 157. C2×C4 | C2×#67 | semidirect |
| 161. C2×C3 | B(4,𝔽2) | semidirect |
| 182. C3 | C2×B(4,𝔽2) | semidirect |
| 187. C2 | #5244 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| C2×#937 | 2 |
| #5244 | 2 |
| C2×#834 | 2 |
| C2×B(4,𝔽2) | 3 |