Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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×C3×C4×D4 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. #5217 | C2 | semidirect |
| 4. #5015 | C2 | semidirect |
| 5. C4×#213 | C2 | semidirect |
| 6. #5007 | C2 | semidirect |
| 7. #4967 | C2 | semidirect |
| 8. #4925 | C2 | semidirect |
| 24. #874 | C22 | semidirect |
| 26. C4×D12 | C22 | semidirect |
| 27. #869 | C22 | semidirect |
| 30. #809 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. C4×C3⋊C8 | C22 | semidirect |
| 35. C2×C4×D4 | D3 | semidirect |
| 106. C3×D4 | #41 | semidirect |
| 113. C2×C3×C4 | D8 | semidirect |
| 192. D4 | #235 | semidirect |
| 201. C2×C4 | #213 | semidirect |
| 234. C3 | #3100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| #5477 | 2 |
| #5217 | 2 |
| #5015 | 2 |
| C4×#213 | 2 |
| #5007 | 2 |
| #4967 | 2 |
| #4925 | 2 |
| #3100 | 3 |