Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 93 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. #4564 | C2 | semidirect |
| 9. C2×C3×Q16 | C4 | semidirect |
| 41. C2×Q16 | Dic3 | semidirect |
| 113. C3 | #2141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| #5106 | 2 |
| C2×#812 | 2 |
| #4564 | 2 |
| #2141 | 3 |