Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 6. C4×C4⋊Dic3 | C2 | semidirect |
| 7. #4928 | C2 | semidirect |
| 8. #4654 | C2 | semidirect |
| 16. C2×C4⋊Dic3 | C4 | semidirect |
| 186. C3 | #2345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic3 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #5212 | 2 |
| #4942 | 2 |
| Dic3×C22⋊C4 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4928 | 2 |
| #4654 | 2 |
| #2345 | 3 |