Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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. #4980 | C2 | semidirect |
| 10. C2×C3×C4⋊C4 | C4 | semidirect |
| 42. C2×C4⋊C4 | Dic3 | semidirect |
| 127. C3 | #2313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| #5212 | 2 |
| #5211 | 2 |
| C4×#217 | 2 |
| #4980 | 2 |
| #2313 | 3 |