Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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×M32 | C2 | semidirect |
| 2. #5115 | C2 | semidirect |
| 3. C2×D48 | C2 | semidirect |
| 4. #4509 | C2 | semidirect |
| 5. #4505 | C2 | semidirect |
| 17. C2×M32 | D3 | semidirect |
| 33. 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×M32 | 2 |
| #5115 | 2 |
| C2×D48 | 2 |
| #4509 | 2 |
| #4505 | 2 |
| #2218 | 3 |