Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 213 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. C22×D24 | C2 | semidirect |
| 2. C2×#874 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. #4695 | C2 | direct (N × H) |
| 11. C2×D24 | C22 | semidirect |
| 13. #874 | C22 | semidirect |
| 14. C3×C4×C8 | C22 | semidirect |
| 18. C2×C4×C8 | D3 | semidirect |
| 27. C2×C3×C8 | D4 | semidirect |
| 40. C4×C8 | C2×D3 | semidirect |
| 45. C2×C3×C4 | D8 | semidirect |
| 53. C3×C8 | C2×D4 | semidirect |
| 63. C2×C8 | D12 | semidirect |
| 74. C3×C4 | C2×D8 | semidirect |
| 83. C2×C4 | D24 | semidirect |
| 88. C8 | C2×D12 | semidirect |
| 89. C2×C3 | #493 | semidirect |
| 100. C4 | C2×D24 | semidirect |
| 102. C3 | C2×#493 | semidirect |
| 104. C2 | #4695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×#874 | 2 |
| C2×C3×C4×C8 | 2 |
| #4695 | 2 |
| C2×#493 | 3 |