Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
236 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#812 | C2 | semidirect |
| 3. #4553 | C2 | direct (N × H) |
| 13. #812 | C22 | semidirect |
| 124. C2×C3 | #349 | semidirect |
| 139. C3 | C2×#349 | semidirect |
| 143. C2 | #4553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C2×#812 | 2 |
| #4553 | 2 |
| C2×#349 | 3 |