Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×#204 | C2 | semidirect |
| 3. C2×C4×Dic6 | C2 | semidirect |
| 4. C2×C3×C4⋊C8 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. #4848 | C2 | direct (N × H) |
| 18. C2×#204 | C22 | semidirect |
| 22. C4×Dic6 | C22 | semidirect |
| 23. C3×C4⋊C8 | C22 | semidirect |
| 24. #821 | C22 | semidirect |
| 29. C2×C4⋊C8 | D3 | semidirect |
| 47. C2×Dic6 | D4 | semidirect |
| 73. C4⋊C8 | C2×D3 | semidirect |
| 81. C2×C3×C4 | SD16 | semidirect |
| 99. Dic6 | C2×D4 | semidirect |
| 138. C3×C4 | C2×SD16 | semidirect |
| 161. C2×C4 | #204 | semidirect |
| 169. C2×C3 | #460 | semidirect |
| 186. C4 | C2×#204 | semidirect |
| 189. C3 | C2×#460 | semidirect |
| 191. C2 | #4848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×#874 | 2 |
| C2×C4×Dic6 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#821 | 2 |
| #4848 | 2 |
| C2×#460 | 3 |