Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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×#216 | C2 | semidirect |
| 4. C2×C3×#101 | C2 | semidirect |
| 5. C2×#824 | C2 | semidirect |
| 7. #4558 | C2 | semidirect |
| 34. C2×#101 | D3 | semidirect |
| 239. C3 | #2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#216 | 2 |
| C2×#942 | 2 |
| C2×#909 | 2 |
| C2×C3×#101 | 2 |
| C2×#824 | 2 |
| #5129 | 2 |
| #4558 | 2 |
| #2020 | 3 |