Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 5. C4×C4⋊Dic3 | C2 | semidirect |
| 6. #4928 | C2 | semidirect |
| 7. #4650 | C2 | semidirect |
| 8. #4648 | C2 | semidirect |
| 15. #926 | C4 | semidirect |
| 182. C3 | #2346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#926 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #5212 | 2 |
| #4944 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4928 | 2 |
| #4650 | 2 |
| #4648 | 2 |
| #2346 | 3 |