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 |
|---|---|---|
| 2. C2×#827 | C2 | semidirect |
| 3. C4×Dic12 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 36. Dic12 | D4 | semidirect |
| 84. C3×C4 | SD32 | semidirect |
| 115. C4 | #827 | semidirect |
| 118. C3 | #2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| C2×#827 | 2 |
| C4×Dic12 | 2 |
| #4562 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2207 | 3 |