Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×Dic3⋊C8 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 6. C3×#336 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 32. #336 | D3 | semidirect |
| 95. C2×C3×C4 | M16 | semidirect |
| 110. C2×Dic3 | M16 | semidirect |
| 200. C2×C4 | ΓL(1,𝔽25) | semidirect |
| 242. C3 | #1851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×Dic3⋊C8 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #1851 | 3 |