Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
250 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 250 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 |
|---|---|---|
| 2. #5237 | C2 | semidirect |
| 3. #4548 | C2 | semidirect |
| 4. #4542 | C2 | semidirect |
| 163. C3 | #2132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5237 | 2 |
| #4548 | 2 |
| #4542 | 2 |
| #2132 | 3 |