Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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. C22×C3×Q16 | C2 | semidirect |
| 2. C2×#828 | C2 | semidirect |
| 4. #4564 | C2 | semidirect |
| 5. #4549 | C2 | semidirect |
| 18. C22×Q16 | D3 | semidirect |
| 33. C3×Q16 | D4 | semidirect |
| 79. Q16 | #67 | semidirect |
| 89. C22×C3 | SD32 | semidirect |
| 126. C22 | #828 | semidirect |
| 133. C3 | #2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×#828 | 2 |
| #5115 | 2 |
| #4564 | 2 |
| #4549 | 2 |
| #2185 | 3 |