Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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×D4×Dic3 | C2 | semidirect |
| 3. #5221 | C2 | semidirect |
| 4. C2×#832 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 14. C2×C3×D8 | C4 | semidirect |
| 45. C2×C3×D4 | C2×C4 | semidirect |
| 59. C2×C3×C8 | C2×C4 | semidirect |
| 77. C2×D8 | Dic3 | semidirect |
| 112. C3×D4 | C22⋊C4 | semidirect |
| 131. C2×Dic3 | D8 | semidirect |
| 145. C2×D4 | C2×Dic3 | semidirect |
| 162. C2×C8 | C2×Dic3 | semidirect |
| 223. D4 | #217 | semidirect |
| 283. C3 | #1879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×D4×Dic3 | 2 |
| #5221 | 2 |
| C2×#832 | 2 |
| #4551 | 2 |
| #4550 | 2 |
| #1879 | 3 |