Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 253 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×C3×C4⋊C4 | C2 | semidirect |
| 4. C22×Dic3⋊C4 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4993 | C2 | direct (N × H) |
| 14. C2×C3×C4⋊C4 | C22 | semidirect |
| 20. C2×Dic3⋊C4 | C22 | semidirect |
| 21. C3⋊#95 | C22 | semidirect |
| 23. C22×C4⋊C4 | D3 | semidirect |
| 61. C2×C4⋊C4 | C2×D3 | semidirect |
| 172. C2×C3 | #399 | semidirect |
| 199. C3 | C2×#399 | semidirect |
| 201. C2 | #4993 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×C3⋊#95 | 2 |
| #4993 | 2 |
| C2×#399 | 3 |