Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 101 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×#834 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. C4×#217 | C2 | semidirect |
| 6. C22×C3×D4 | C4 | semidirect |
| 13. C2×C3×C4⋊C4 | C4 | semidirect |
| 14. C2×C3×C22⋊C4 | C4 | semidirect |
| 51. #217 | D4 | semidirect |
| 54. C22×D4 | Dic3 | semidirect |
| 62. C2×C4⋊C4 | Dic3 | semidirect |
| 65. C2×C22⋊C4 | Dic3 | semidirect |
| 153. C3×C4 | #99 | semidirect |
| 221. C4 | #834 | semidirect |
| 222. C3 | #1964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| C2×#834 | 2 |
| #5212 | 2 |
| C4×#217 | 2 |
| #1964 | 3 |