Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#904 | C2 | semidirect |
| 2. C22×C3×C16 | C2 | semidirect |
| 3. C2×Dic24 | C2 | semidirect |
| 4. #4904 | C2 | direct (N × H) |
| 5. C2×#800 | C2 | semidirect |
| 6. C2×D48 | C2 | semidirect |
| 12. #904 | C22 | semidirect |
| 17. C2×C3×C16 | C22 | semidirect |
| 18. Dic24 | C22 | semidirect |
| 19. #800 | C22 | semidirect |
| 20. D48 | C22 | semidirect |
| 26. C22×C16 | D3 | semidirect |
| 57. C2×C16 | C2×D3 | semidirect |
| 118. C2×C3 | #508 | semidirect |
| 130. C3 | C2×#508 | semidirect |
| 133. C2 | #4904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C22×C3×C16 | 2 |
| C2×Dic24 | 2 |
| #4904 | 2 |
| C2×#800 | 2 |
| C2×D48 | 2 |
| C2×#508 | 3 |