Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 213 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×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×C3×C4⋊C8 | C2 | semidirect |
| 4. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 6. #4838 | C2 | direct (N × H) |
| 17. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 20. C3×C4⋊C8 | C22 | semidirect |
| 21. (C2×D3)⋊C8 | C22 | semidirect |
| 22. C4×C3⋊C8 | C22 | semidirect |
| 26. C2×C4⋊C8 | D3 | semidirect |
| 47. C2×C3⋊C8 | D4 | semidirect |
| 63. C4⋊C8 | C2×D3 | semidirect |
| 72. C2×C3×C4 | M16 | semidirect |
| 87. C3⋊C8 | C2×D4 | semidirect |
| 120. C3×C4 | C2×M16 | semidirect |
| 136. C2×C4 | ΓL(1,𝔽25) | semidirect |
| 146. C2×C3 | #436 | semidirect |
| 162. C4 | C2×ΓL(1,𝔽25) | semidirect |
| 165. C3 | C2×#436 | semidirect |
| 167. C2 | #4838 | direct (N × H) |
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×C4×D12 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4838 | 2 |
| C2×#436 | 3 |