Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 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×C3×C22⋊C4 | C2 | semidirect |
| 3. C22×#217 | C2 | semidirect |
| 4. #5213 | C2 | semidirect |
| 5. #4958 | C2 | semidirect |
| 6. #4955 | C2 | semidirect |
| 7. #4943 | C2 | semidirect |
| 11. C23×C3×C4 | C22 | semidirect |
| 14. C22×#67 | C4 | semidirect |
| 18. C23×Dic3 | C22 | semidirect |
| 21. C2×C3×C22⋊C4 | C22 | semidirect |
| 24. C2×#217 | C22 | semidirect |
| 25. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 26. C3⋊#95 | C22 | semidirect |
| 29. C22×C22⋊C4 | D3 | semidirect |
| 44. C23×D3 | C2×C4 | semidirect |
| 54. C2×#67 | C2×C4 | semidirect |
| 55. C2×#67 | C2×C4 | semidirect |
| 60. C22×Dic3 | C2×C4 | semidirect |
| 77. C23×C4 | C2×D3 | semidirect |
| 84. C2×C22⋊C4 | C2×D3 | semidirect |
| 92. C23×C3 | C22⋊C4 | semidirect |
| 196. C23 | (C2×D3)⋊C4 | semidirect |
| 252. C3 | #2308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#67 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| #5213 | 2 |
| #4958 | 2 |
| #4955 | 2 |
| #4943 | 2 |
| #2308 | 3 |