Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #4837 | C2 | semidirect |
| 3. C4×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×Q8⋊C8 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4483 | C2 | semidirect |
| 7. #4459 | C2 | semidirect |
| 32. Q8⋊C8 | D3 | semidirect |
| 88. C3×Q8 | M16 | semidirect |
| 100. D12 | M16 | semidirect |
| 166. Q8 | ΓL(1,𝔽25) | semidirect |
| 215. C3 | #1489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#239 | 2 |
| #4837 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| C3×Q8⋊C8 | 2 |
| #4535 | 2 |
| #4483 | 2 |
| #4459 | 2 |
| #1489 | 3 |