Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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. C23×C3⋊C8 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. C2×#830 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 31. C2×C3×D4 | C8 | semidirect |
| 56. C2×C3⋊C8 | D4 | semidirect |
| 80. C23×C3 | C2×C8 | semidirect |
| 98. C2×C3×C4 | C2×C8 | semidirect |
| 109. C2×D4 | C3⋊C8 | semidirect |
| 144. C22×C3 | C22⋊C8 | semidirect |
| 164. C23 | C2×C3⋊C8 | semidirect |
| 182. C2×C4 | C2×C3⋊C8 | semidirect |
| 206. C22 | #830 | semidirect |
| 219. C3 | #1869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#830 | 2 |
| #4524 | 2 |
| #1869 | 3 |