Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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. C3×#417 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 6. #4988 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 13. #1009 | C4 | semidirect |
| 21. C2×C3×M16 | C22 | semidirect |
| 22. C2×C3×C4⋊C4 | C22 | semidirect |
| 24. C2×C4×Dic3 | C22 | semidirect |
| 25. C2×#208 | C22 | semidirect |
| 37. #417 | D3 | semidirect |
| 104. C2×M16 | C2×D3 | semidirect |
| 105. C2×C4⋊C4 | C2×D3 | semidirect |
| 127. C3×Q8 | C22⋊C4 | semidirect |
| 131. C3×D4 | C22⋊C4 | semidirect |
| 156. D12 | C22⋊C4 | semidirect |
| 161. Dic6 | C22⋊C4 | semidirect |
| 254. Q8 | (C2×D3)⋊C4 | semidirect |
| 268. D4 | (C2×D3)⋊C4 | semidirect |
| 322. C3 | #1792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C3×#417 | 2 |
| C2×#837 | 2 |
| C2×#825 | 2 |
| C2×#823 | 2 |
| #4988 | 2 |
| #4966 | 2 |
| #1792 | 3 |