Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5728 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. #5076 | C2 | semidirect |
| 6. #4776 | C2 | semidirect |
| 7. #4762 | C2 | semidirect |
| 8. #4693 | C2 | semidirect |
| 9. #4685 | C2 | semidirect |
| 14. C3×C4⋊Q8 | C22 | semidirect |
| 21. C2×#214 | C22 | semidirect |
| 22. C2×#204 | C22 | semidirect |
| 26. #887 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. C3×#102 | C22 | semidirect |
| 31. C3×C4×C8 | C22 | semidirect |
| 33. Dic3⋊C8 | C22 | semidirect |
| 34. #809 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 41. #486 | D3 | semidirect |
| 85. C4⋊Q8 | C2×D3 | semidirect |
| 100. #102 | C2×D3 | semidirect |
| 103. C4×C8 | C2×D3 | semidirect |
| 130. C4×D3 | SD16 | semidirect |
| 242. C3 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×#127 | 2 |
| C3×#486 | 2 |
| #5088 | 2 |
| #5076 | 2 |
| #4776 | 2 |
| #4762 | 2 |
| #4693 | 2 |
| #4685 | 2 |
| #3208 | 3 |