Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5507 | C2 | semidirect |
| 2. C2×C3×#107 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. C8×#67 | C2 | semidirect |
| 5. #4967 | C2 | semidirect |
| 6. #4890 | C2 | semidirect |
| 7. #4883 | C2 | semidirect |
| 8. #4882 | C2 | semidirect |
| 9. D3×#107 | C2 | semidirect |
| 10. #4874 | C2 | semidirect |
| 11. #4872 | C2 | semidirect |
| 50. C2×#107 | D3 | semidirect |
| 120. #67 | D8 | semidirect |
| 134. C3×C8 | #41 | semidirect |
| 214. C8 | #235 | semidirect |
| 240. C3 | #3334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5507 | 2 |
| C2×C3×#107 | 2 |
| #5115 | 2 |
| C8×#67 | 2 |
| #4967 | 2 |
| #4890 | 2 |
| #4883 | 2 |
| #4882 | 2 |
| D3×#107 | 2 |
| #4874 | 2 |
| #4872 | 2 |
| #3334 | 3 |