Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
| 2. #5115 | C2 | semidirect |
| 3. C2×D48 | C2 | semidirect |
| 4. #4509 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 17. C22×C16 | D3 | semidirect |
| 33. C3×C16 | D4 | semidirect |
| 68. C16 | #67 | semidirect |
| 71. C22×C3 | D16 | semidirect |
| 103. C22 | D48 | semidirect |
| 109. C3 | #2215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C16 | 2 |
| #5115 | 2 |
| C2×D48 | 2 |
| #4509 | 2 |
| #4504 | 2 |
| #2215 | 3 |