Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #5574 | C2 | semidirect |
| 3. C3×#441 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 5. C4×#215 | C2 | semidirect |
| 6. #4869 | C2 | semidirect |
| 7. D3×#106 | C2 | semidirect |
| 8. #4803 | C2 | semidirect |
| 9. #4788 | C2 | semidirect |
| 10. #4711 | C2 | semidirect |
| 11. #4708 | C2 | semidirect |
| 18. #919 | C4 | semidirect |
| 46. #441 | D3 | semidirect |
| 54. #239 | C2×C4 | semidirect |
| 62. C3×Q16 | C2×C4 | semidirect |
| 69. #215 | C2×C4 | semidirect |
| 81. D24 | C2×C4 | semidirect |
| 83. D3×C8 | C2×C4 | semidirect |
| 146. Q16 | C4×D3 | semidirect |
| 224. C3 | #2952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| #5574 | 2 |
| C3×#441 | 2 |
| #5184 | 2 |
| C4×#215 | 2 |
| #4869 | 2 |
| D3×#106 | 2 |
| #4803 | 2 |
| #4788 | 2 |
| #4711 | 2 |
| #4708 | 2 |
| #2952 | 3 |