Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×D8 | C2 | semidirect |
| 2. C2×#826 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. #4549 | C2 | semidirect |
| 13. C2×D24 | C22 | semidirect |
| 16. #818 | C22 | semidirect |
| 17. C2×C3⋊C16 | C22 | semidirect |
| 18. C22×D8 | D3 | semidirect |
| 33. C3×D8 | D4 | semidirect |
| 82. D8 | #67 | semidirect |
| 95. C22×C3 | D16 | semidirect |
| 138. C22 | #826 | semidirect |
| 144. C3 | #2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×#826 | 2 |
| #5115 | 2 |
| #4562 | 2 |
| #4549 | 2 |
| #2184 | 3 |