Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22×C3⋊C16 | C2 | semidirect |
| 3. C2×#798 | C2 | semidirect |
| 4. C3×C22⋊C16 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 6. #4502 | C2 | semidirect |
| 7. Dic3⋊C16 | C2 | semidirect |
| 27. C22⋊C16 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 99. C22×C3 | M32 | semidirect |
| 137. C22 | #798 | semidirect |
| 145. C3 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#67 | 2 |
| C22×C3⋊C16 | 2 |
| C2×#798 | 2 |
| C3×C22⋊C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| #4502 | 2 |
| Dic3⋊C16 | 2 |
| #2168 | 3 |