Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×D3×Q8 | C2 | semidirect |
| 2. C2×#918 | C2 | semidirect |
| 4. C3×#451 | C2 | semidirect |
| 5. #5227 | C2 | semidirect |
| 6. #5186 | C2 | semidirect |
| 7. #5050 | C2 | semidirect |
| 8. #4806 | C2 | semidirect |
| 9. #4802 | C2 | semidirect |
| 10. #4738 | C2 | semidirect |
| 11. #4726 | C2 | semidirect |
| 24. C2×C3×Q16 | C22 | semidirect |
| 27. C2×#216 | C22 | semidirect |
| 28. C2×#215 | C22 | semidirect |
| 31. C2×#204 | C22 | semidirect |
| 39. C3×#103 | C22 | semidirect |
| 41. #835 | C22 | semidirect |
| 44. #816 | C22 | semidirect |
| 45. #810 | C22 | semidirect |
| 51. #451 | D3 | semidirect |
| 73. D3×Q8 | D4 | semidirect |
| 122. C2×Q16 | C2×D3 | semidirect |
| 138. #103 | C2×D3 | semidirect |
| 238. C22×C3 | #137 | semidirect |
| 249. C2×D3 | #137 | semidirect |
| 320. C22 | #918 | semidirect |
| 331. C3 | #3004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×#918 | 2 |
| #5627 | 2 |
| C3×#451 | 2 |
| #5227 | 2 |
| #5186 | 2 |
| #5050 | 2 |
| #4806 | 2 |
| #4802 | 2 |
| #4738 | 2 |
| #4726 | 2 |
| #3004 | 3 |