Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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. #4933 | C2 | semidirect |
| 7. C4×Dic3⋊C4 | C2 | semidirect |
| 8. #4653 | C2 | semidirect |
| 9. #4646 | C2 | semidirect |
| 20. #924 | C4 | semidirect |
| 224. C3 | #2332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#924 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #5211 | 2 |
| #4945 | 2 |
| #4944 | 2 |
| #4933 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4653 | 2 |
| #4646 | 2 |
| #2332 | 3 |