Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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×#835 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. #5212 | C2 | semidirect |
| 5. C2×#830 | C2 | semidirect |
| 10. C2×C3×#41 | C4 | semidirect |
| 62. C2×#41 | Dic3 | semidirect |
| 88. C3×Q8 | C22⋊C4 | semidirect |
| 92. C3×D4 | C22⋊C4 | semidirect |
| 174. Q8 | #217 | semidirect |
| 178. D4 | #217 | semidirect |
| 223. C3 | #1788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| #5212 | 2 |
| C2×#830 | 2 |
| #1788 | 3 |