Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#951 | C2 | semidirect |
| 3. C2×#936 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 6. #5004 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 61. C2×Dic6 | D4 | semidirect |
| 70. C4×Dic3 | D4 | semidirect |
| 74. #208 | D4 | semidirect |
| 256. C3 | #2004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| C2×#951 | 2 |
| C2×#936 | 2 |
| C2×#837 | 2 |
| C2×#833 | 2 |
| #5004 | 2 |
| #4532 | 2 |
| #2004 | 3 |