Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×Dic6 | C2 | semidirect |
| 4. C4×#217 | C2 | semidirect |
| 5. #4985 | C2 | semidirect |
| 6. #4953 | C2 | semidirect |
| 7. #4947 | C2 | semidirect |
| 8. #4932 | C2 | semidirect |
| 187. C3 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C2×C4×Dic6 | 2 |
| #5222 | 2 |
| C4×#217 | 2 |
| #4985 | 2 |
| #4953 | 2 |
| #4947 | 2 |
| #4932 | 2 |
| #2398 | 3 |