Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×C3×C4×D4 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C2×#874 | C2 | semidirect |
| 4. #5015 | C2 | direct (N × H) |
| 5. C2×#809 | C2 | semidirect |
| 6. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 14. C3×C4×D4 | C22 | semidirect |
| 19. C2×#213 | C22 | semidirect |
| 22. #874 | C22 | semidirect |
| 23. #809 | C22 | semidirect |
| 24. C4⋊(C3⋊C8) | C22 | semidirect |
| 27. C2×C4×D4 | D3 | semidirect |
| 35. C2×C3×D4 | D4 | semidirect |
| 70. C4×D4 | C2×D3 | semidirect |
| 87. C3×D4 | C2×D4 | semidirect |
| 92. C2×C3×C4 | D8 | semidirect |
| 117. C2×D4 | D12 | semidirect |
| 148. C3×C4 | C2×D8 | semidirect |
| 167. D4 | C2×D12 | semidirect |
| 172. C2×C4 | #213 | semidirect |
| 181. C2×C3 | #459 | semidirect |
| 201. C4 | C2×#213 | semidirect |
| 204. C3 | C2×#459 | semidirect |
| 207. C2 | #5015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C22×#213 | 2 |
| C2×#874 | 2 |
| #5015 | 2 |
| C2×#809 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#459 | 3 |