Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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⋊Q8 | C2 | semidirect |
| 2. C2×#942 | C2 | semidirect |
| 4. #5092 | C2 | semidirect |
| 5. #5086 | C2 | semidirect |
| 6. #5085 | C2 | semidirect |
| 7. C4×#208 | C2 | semidirect |
| 29. C2×C4⋊Q8 | D3 | semidirect |
| 55. #208 | D4 | semidirect |
| 125. C3×C4 | #137 | semidirect |
| 160. C4 | #942 | semidirect |
| 162. C3 | #3152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C2×#942 | 2 |
| #5477 | 2 |
| #5092 | 2 |
| #5086 | 2 |
| #5085 | 2 |
| C4×#208 | 2 |
| #3152 | 3 |