Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. C2×C3×#107 | C2 | semidirect |
| 5. C2×#817 | C2 | semidirect |
| 6. C2×#808 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4881 | C2 | direct (N × H) |
| 21. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 27. C3×#107 | C22 | semidirect |
| 28. #817 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 30. #807 | C22 | semidirect |
| 36. C2×#107 | D3 | semidirect |
| 52. C2×C3×C8 | C2×C4 | semidirect |
| 65. C2×C3⋊C8 | C2×C4 | semidirect |
| 67. ΓL(1,𝔽25) | C2×C4 | semidirect |
| 86. #107 | C2×D3 | semidirect |
| 112. C3×C8 | C22×C4 | semidirect |
| 113. C3⋊C8 | C22×C4 | semidirect |
| 130. C2×C8 | C4×D3 | semidirect |
| 183. C8 | C2×C4×D3 | semidirect |
| 184. C2×C3 | #428 | semidirect |
| 205. C3 | C2×#428 | semidirect |
| 207. C2 | #4881 | 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×#892 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#107 | 2 |
| C2×#817 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| #4881 | 2 |
| C2×#428 | 3 |