Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. C3×#519 | C2 | semidirect |
| 4. #5225 | C2 | semidirect |
| 5. #5026 | C2 | semidirect |
| 6. C4×#215 | C2 | semidirect |
| 8. #4998 | C2 | semidirect |
| 9. #4997 | C2 | semidirect |
| 14. C3×C4×Q8 | C22 | semidirect |
| 18. C2×#215 | C4 | semidirect |
| 27. #835 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 30. #807 | C22 | semidirect |
| 31. #803 | C22 | semidirect |
| 32. C4×C3⋊C8 | C22 | semidirect |
| 34. #519 | D3 | semidirect |
| 45. C2×C3×Q8 | C2×C4 | semidirect |
| 63. #215 | C2×C4 | semidirect |
| 64. #215 | C2×C4 | semidirect |
| 69. C2×C3⋊C8 | C2×C4 | semidirect |
| 81. C4×Q8 | C2×D3 | semidirect |
| 121. C2×Q8 | C4×D3 | semidirect |
| 202. C3 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#519 | 2 |
| C22×#215 | 2 |
| #5521 | 2 |
| #5225 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #5001 | 2 |
| #4998 | 2 |
| #4997 | 2 |
| #2949 | 3 |