Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#815 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 12. C22×C3⋊C8 | C4 | semidirect |
| 15. C3×C22⋊C8 | C4 | semidirect |
| 50. C22⋊C8 | Dic3 | semidirect |
| 72. C3⋊C8 | C22⋊C4 | semidirect |
| 95. C22×C3 | #97 | semidirect |
| 133. C22 | #815 | semidirect |
| 143. C3 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊C8 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C4×#217 | 2 |
| C2×#815 | 2 |
| #4550 | 2 |
| #1752 | 3 |