Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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. C3×#466 | C2 | semidirect |
| 2. C2×#826 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. C22×C3⋊C16 | C2 | semidirect |
| 5. #4562 | C2 | semidirect |
| 6. #4491 | C2 | semidirect |
| 7. #4489 | C2 | semidirect |
| 25. #466 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 103. C22×C3 | D16 | semidirect |
| 145. C22 | #826 | semidirect |
| 152. C3 | #2215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#466 | 2 |
| C2×#826 | 2 |
| #5115 | 2 |
| C22×C3⋊C16 | 2 |
| #4562 | 2 |
| #4491 | 2 |
| #4489 | 2 |
| #2215 | 3 |