Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#1004 | C2 | semidirect |
| 2. C2×#940 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. C2×C3×#100 | C2 | semidirect |
| 5. C2×#825 | C2 | semidirect |
| 6. #4747 | C2 | direct (N × H) |
| 13. #1004 | C22 | semidirect |
| 17. C22×D12 | C22 | semidirect |
| 18. C2×C3×M16 | C22 | semidirect |
| 20. #940 | C22 | semidirect |
| 21. C2×C4×Dic3 | C22 | semidirect |
| 23. #908 | C22 | semidirect |
| 26. C3×#100 | C22 | semidirect |
| 27. #825 | C22 | semidirect |
| 33. C2×#100 | D3 | semidirect |
| 56. #235 | D4 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 62. C2×D12 | C23 | semidirect |
| 64. C2×Dic6 | D4 | semidirect |
| 66. C3×M16 | C23 | semidirect |
| 69. C4×Dic3 | C23 | semidirect |
| 86. C2×M16 | C2×D3 | semidirect |
| 91. #100 | C2×D3 | semidirect |
| 121. D12 | C2×D4 | semidirect |
| 125. Dic6 | C2×D4 | semidirect |
| 161. M16 | C22×D3 | semidirect |
| 222. C2×C3 | #453 | semidirect |
| 245. C3 | C2×#453 | semidirect |
| 251. C2 | #4747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| C2×#940 | 2 |
| C2×#908 | 2 |
| C2×C3×#100 | 2 |
| C2×#825 | 2 |
| #4747 | 2 |
| C2×#453 | 3 |