Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#800 | C2 | semidirect |
| 2. C4×Dic12 | C2 | semidirect |
| 4. C3×C4⋊C16 | C2 | semidirect |
| 5. #4509 | C2 | semidirect |
| 20. C4⋊C16 | D3 | semidirect |
| 33. Dic12 | D4 | semidirect |
| 84. C3×C4 | SD32 | semidirect |
| 115. C4 | #800 | semidirect |
| 118. C3 | #2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#800 | 2 |
| C4×Dic12 | 2 |
| #4695 | 2 |
| C3×C4⋊C16 | 2 |
| #4509 | 2 |
| #2207 | 3 |