Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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 |
|---|---|---|
| 3. C22×Dic3⋊C4 | C2 | semidirect |
| 4. C2×C3×#95 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4667 | C2 | direct (N × H) |
| 14. C22×C4×D3 | C4 | semidirect |
| 19. C2×Dic3⋊C4 | C22 | semidirect |
| 20. C3×#95 | C22 | semidirect |
| 21. C3⋊#95 | C22 | semidirect |
| 27. C2×#95 | D3 | semidirect |
| 51. C2×C4×D3 | C2×C4 | semidirect |
| 67. #95 | C2×D3 | semidirect |
| 80. C22×D3 | C4⋊C4 | semidirect |
| 95. C2×Dic3 | C22⋊C4 | semidirect |
| 140. C2×D3 | C2×C4⋊C4 | semidirect |
| 144. Dic3 | C2×C22⋊C4 | semidirect |
| 176. C2×C3 | #380 | semidirect |
| 203. C3 | C2×#380 | semidirect |
| 205. C2 | #4667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×C3×#95 | 2 |
| C2×C3⋊#95 | 2 |
| #4667 | 2 |
| C2×#380 | 3 |