Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×#893 | C2 | semidirect |
| 3. C2×C3×#106 | C2 | semidirect |
| 4. C2×#815 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. #4869 | C2 | direct (N × H) |
| 15. C2×D24 | C4 | semidirect |
| 18. #893 | C22 | semidirect |
| 19. C3×#106 | C22 | semidirect |
| 20. #815 | C22 | semidirect |
| 21. #809 | C22 | semidirect |
| 25. C2×#106 | D3 | semidirect |
| 34. C2×D12 | C2×C4 | semidirect |
| 38. C2×C3×C8 | C2×C4 | semidirect |
| 47. D24 | C2×C4 | semidirect |
| 59. #106 | C2×D3 | semidirect |
| 77. D12 | C22×C4 | semidirect |
| 79. C3×C8 | C22×C4 | semidirect |
| 94. C2×C8 | C4×D3 | semidirect |
| 131. C8 | C2×C4×D3 | semidirect |
| 132. C2×C3 | #442 | semidirect |
| 148. C3 | C2×#442 | semidirect |
| 150. C2 | #4869 | 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×#893 | 2 |
| C2×C3×#106 | 2 |
| C2×#815 | 2 |
| C2×#809 | 2 |
| #4869 | 2 |
| C2×#442 | 3 |