Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 3. C2×#836 | C2 | semidirect |
| 5. #4552 | C2 | semidirect |
| 21. C22×Q16 | D3 | semidirect |
| 154. C3 | #2020 | 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×#942 | 2 |
| C2×#836 | 2 |
| #5110 | 2 |
| #4552 | 2 |
| #2020 | 3 |