Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#127 | C2 | semidirect |
| 2. C22×#214 | C2 | semidirect |
| 3. C22×#213 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. #5074 | C2 | direct (N × H) |
| 6. C2×#803 | C2 | semidirect |
| 13. C3×#127 | C22 | semidirect |
| 16. C2×#214 | C22 | semidirect |
| 18. C2×#213 | C22 | semidirect |
| 22. #875 | C22 | semidirect |
| 23. #803 | C22 | semidirect |
| 26. C2×#127 | D3 | semidirect |
| 52. C2×C3⋊C8 | D4 | semidirect |
| 64. #127 | C2×D3 | semidirect |
| 92. C3⋊C8 | C2×D4 | semidirect |
| 154. C2×C3 | #496 | semidirect |
| 171. C3 | C2×#496 | semidirect |
| 174. C2 | #5074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| C22×#214 | 2 |
| C22×#213 | 2 |
| C2×#875 | 2 |
| #5074 | 2 |
| C2×#803 | 2 |
| C2×#496 | 3 |