Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 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×#949 | C2 | semidirect |
| 3. C2×#940 | C2 | semidirect |
| 4. #5241 | C2 | direct (N × H) |
| 5. C2×#837 | C2 | semidirect |
| 6. C2×#833 | C2 | semidirect |
| 10. C3×H(5,𝔽2) | C22 | semidirect |
| 17. C22×D12 | C22 | semidirect |
| 19. #949 | C22 | semidirect |
| 22. #940 | C22 | semidirect |
| 24. C2×C4×Dic3 | C22 | semidirect |
| 25. C2×#208 | C22 | semidirect |
| 26. #837 | C22 | semidirect |
| 27. #833 | C22 | semidirect |
| 28. C2×H(5,𝔽2) | D3 | semidirect |
| 41. C3×#41 | D4 | semidirect |
| 43. C2×C3×Q8 | D4 | semidirect |
| 53. C2×C3×D4 | D4 | semidirect |
| 64. C2×D12 | C23 | semidirect |
| 68. C4×Dic3 | C23 | semidirect |
| 70. #208 | C23 | semidirect |
| 74. H(5,𝔽2) | C2×D3 | semidirect |
| 105. C3×Q8 | C2×D4 | semidirect |
| 112. C3×D4 | C2×D4 | semidirect |
| 134. #41 | #67 | semidirect |
| 136. C2×Q8 | #67 | semidirect |
| 152. C2×D4 | #67 | semidirect |
| 197. Q8 | C2×#67 | semidirect |
| 207. D4 | C2×#67 | semidirect |
| 223. C2×C3 | #453 | semidirect |
| 245. C3 | C2×#453 | semidirect |
| 251. C2 | #5241 | 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×#949 | 2 |
| C2×#940 | 2 |
| #5241 | 2 |
| C2×#837 | 2 |
| C2×#833 | 2 |
| C2×#453 | 3 |