Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5521 | C2 | semidirect |
| 3. C3×#421 | C2 | semidirect |
| 4. #5236 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 6. #4557 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 13. #947 | C4 | semidirect |
| 14. #940 | C4 | semidirect |
| 29. #421 | D3 | semidirect |
| 38. C2×C3×Q8 | C2×C4 | semidirect |
| 40. C2×C3×D4 | C2×C4 | semidirect |
| 56. C3×C42 | D4 | semidirect |
| 63. C4×Dic3 | C2×C4 | semidirect |
| 64. C4×Dic3 | D4 | semidirect |
| 122. C2×Q8 | C4×D3 | semidirect |
| 131. C2×D4 | C4×D3 | semidirect |
| 151. C42 | #67 | semidirect |
| 226. C3 | #1911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5830 | 2 |
| #5521 | 2 |
| C3×#421 | 2 |
| #5236 | 2 |
| C2×#823 | 2 |
| #4557 | 2 |
| #4531 | 2 |
| #1911 | 3 |