Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×C3×D16 | C2 | semidirect |
| 2. #5157 | C2 | semidirect |
| 3. C2×#798 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. #4505 | C2 | semidirect |
| 16. C2×D16 | D3 | semidirect |
| 32. C3×C16 | D4 | semidirect |
| 68. C16 | #67 | semidirect |
| 106. C3 | #2218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| #5157 | 2 |
| C2×#798 | 2 |
| #4562 | 2 |
| #4505 | 2 |
| #2218 | 3 |