Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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×Q16 | C2 | semidirect |
| 3. C2×Q8×Dic3 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. #5185 | C2 | direct (N × H) |
| 8. C2×Dic3⋊C8 | C2 | semidirect |
| 14. C2×C3×Q16 | C22 | semidirect |
| 19. Q8×Dic3 | C22 | semidirect |
| 29. #835 | C22 | semidirect |
| 31. Dic3⋊C8 | C22 | semidirect |
| 32. C22×Q16 | D3 | semidirect |
| 77. C2×Q16 | C2×D3 | semidirect |
| 204. C2×C3 | #464 | semidirect |
| 225. C3 | C2×#464 | semidirect |
| 227. C2 | #5185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×#947 | 2 |
| C2×Q8×Dic3 | 2 |
| C22×#215 | 2 |
| C2×#835 | 2 |
| #5185 | 2 |
| C2×#821 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#464 | 3 |