Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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. #5822 | C2 | semidirect |
| 3. #5805 | C2 | semidirect |
| 4. #5242 | C2 | semidirect |
| 5. #5241 | C2 | semidirect |
| 6. #5236 | C2 | semidirect |
| 7. C2×#833 | C2 | semidirect |
| 17. C2×#235 | C22 | semidirect |
| 19. #951 | C22 | semidirect |
| 21. #949 | C22 | semidirect |
| 23. #940 | C22 | semidirect |
| 25. #936 | C22 | semidirect |
| 27. #926 | C22 | semidirect |
| 28. C2×#208 | C22 | semidirect |
| 29. #837 | C22 | semidirect |
| 30. #833 | C22 | semidirect |
| 31. C2×H(5,𝔽2) | D3 | semidirect |
| 44. C3×#41 | D4 | semidirect |
| 46. C2×C3×Q8 | D4 | semidirect |
| 56. C2×C3×D4 | D4 | semidirect |
| 65. C2×D12 | C23 | semidirect |
| 67. C2×Dic6 | C23 | semidirect |
| 75. C4×Dic3 | C23 | semidirect |
| 77. #208 | C23 | semidirect |
| 144. #41 | #67 | semidirect |
| 147. C2×Q8 | #67 | semidirect |
| 160. C2×D4 | #67 | semidirect |
| 255. C3 | #3019 | semidirect |
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 |
| #5822 | 2 |
| #5805 | 2 |
| #5242 | 2 |
| #5241 | 2 |
| #5236 | 2 |
| C2×#833 | 2 |
| #3019 | 3 |