Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. C22×C3×C16 | C2 | semidirect |
| 3. C2×D3×C16 | C2 | semidirect |
| 4. #4549 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 6. Dic3⋊C16 | C2 | semidirect |
| 7. Dic3×C16 | C2 | semidirect |
| 23. C22×C16 | D3 | semidirect |
| 45. C3×C16 | D4 | semidirect |
| 67. #67 | C16 | direct (N × H) |
| 96. C16 | #67 | direct (N × H) |
| 99. C22×C3 | C2×C16 | semidirect |
| 103. C2×D3 | C2×C16 | semidirect |
| 109. Dic3 | C2×C16 | semidirect |
| 137. C22 | D3×C16 | semidirect |
| 145. C3 | D4×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C16 | 2 |
| C8×#67 | 2 |
| C2×D3×C16 | 2 |
| #4549 | 2 |
| (C2×D3)⋊C16 | 2 |
| Dic3⋊C16 | 2 |
| Dic3×C16 | 2 |
| D4×C16 | 3 |