Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
598 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#217 | C2 | semidirect |
| 3. #5247 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. #4526 | C2 | semidirect |
| 8. C22×C3×D4 | C4 | semidirect |
| 14. C2×C3×C22⋊C4 | C4 | semidirect |
| 31. C24×C3 | C2×C4 | semidirect |
| 43. C22×C3×C4 | C2×C4 | semidirect |
| 44. C22×C3×C4 | C2×C4 | semidirect |
| 58. #217 | D4 | semidirect |
| 60. C22×D4 | Dic3 | semidirect |
| 71. C2×C22⋊C4 | Dic3 | semidirect |
| 117. C24 | C2×Dic3 | semidirect |
| 133. C22×C4 | C2×Dic3 | semidirect |
| 134. C22×C4 | C2×Dic3 | semidirect |
| 164. C22×C3 | #99 | semidirect |
| 241. C22 | #834 | semidirect |
| 251. C3 | #1898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#120 | 2 |
| C22×#217 | 2 |
| #5247 | 2 |
| C2×#834 | 2 |
| #4526 | 2 |
| #1898 | 3 |