Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 1. C24×C3×C4 | C2 | semidirect |
| 3. C2×C4×#67 | C2 | semidirect |
| 4. #5247 | C2 | semidirect |
| 5. #5213 | C2 | semidirect |
| 6. #5210 | C2 | semidirect |
| 7. C4×#217 | C2 | semidirect |
| 14. C22×C4×D3 | C22 | semidirect |
| 15. #953 | C4 | direct (N × H) |
| 20. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 21. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C2×C4×Dic3 | C22 | semidirect |
| 23. C3⋊#95 | C22 | semidirect |
| 24. C24×C4 | D3 | semidirect |
| 33. C24×C3 | C2×C4 | semidirect |
| 40. C22×C3×C4 | D4 | semidirect |
| 45. C2×#67 | C2×C4 | semidirect |
| 52. #217 | C2×C4 | semidirect |
| 82. C22×D3 | C22×C4 | semidirect |
| 94. C2×Dic3 | C22×C4 | semidirect |
| 99. C24 | C4×D3 | semidirect |
| 112. C22×C4 | #67 | semidirect |
| 126. C22×C3 | C4×D4 | semidirect |
| 134. C3×C4 | #120 | semidirect |
| 176. C22 | C4×#67 | semidirect |
| 184. C4 | #953 | direct (N × H) |
| 185. C3 | C4×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C2×#953 | 2 |
| C2×C4×#67 | 2 |
| #5247 | 2 |
| #5213 | 2 |
| #5210 | 2 |
| C4×#217 | 2 |
| C4×#120 | 3 |