Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 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. #5486 | C2 | semidirect |
| 3. C2×C3×#99 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. C2×#806 | C2 | semidirect |
| 6. #4527 | C2 | semidirect |
| 7. #4526 | C2 | semidirect |
| 13. #953 | C4 | semidirect |
| 20. #929 | C4 | semidirect |
| 32. C2×#99 | D3 | semidirect |
| 35. C24×C3 | C2×C4 | semidirect |
| 46. C22×C3×C4 | C2×C4 | semidirect |
| 62. C3×C22⋊C4 | D4 | semidirect |
| 68. #217 | C2×C4 | semidirect |
| 69. #217 | D4 | semidirect |
| 137. C24 | C4×D3 | semidirect |
| 159. C22×C4 | C4×D3 | semidirect |
| 174. C22⋊C4 | #67 | semidirect |
| 286. C3 | #1913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5804 | 2 |
| #5486 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| C2×#806 | 2 |
| #4527 | 2 |
| #4526 | 2 |
| #1913 | 3 |