Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 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×C4⋊C4 | C2 | semidirect |
| 3. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4991 | C2 | direct (N × H) |
| 17. C2×C3×C4⋊C4 | C22 | semidirect |
| 20. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 22. C3⋊#95 | C22 | semidirect |
| 24. C22×C4⋊C4 | D3 | semidirect |
| 44. C22×C3×C4 | D4 | semidirect |
| 67. C2×C4⋊C4 | C2×D3 | semidirect |
| 102. C2×C3×C4 | C2×D4 | semidirect |
| 129. C22×C4 | D12 | semidirect |
| 192. C2×C4 | C2×D12 | semidirect |
| 194. C2×C3 | #394 | semidirect |
| 223. C3 | C2×#394 | semidirect |
| 225. C2 | #4991 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C2×C3⋊#95 | 2 |
| #4991 | 2 |
| C2×#394 | 3 |