Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #4452 | C2 | semidirect |
| 7. C22×Dic6 | C4 | semidirect |
| 11. C2×C4⋊Dic3 | C4 | semidirect |
| 14. #924 | C4 | semidirect |
| 182. C3 | #1508 | 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 |
| #5207 | 2 |
| #4452 | 2 |
| #1508 | 3 |