Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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. #5196 | C2 | semidirect |
| 3. #5195 | C2 | semidirect |
| 4. #5155 | C2 | semidirect |
| 5. #4563 | C2 | semidirect |
| 6. #4517 | C2 | semidirect |
| 7. #4511 | C2 | semidirect |
| 144. C3 | #2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#509 | 2 |
| #5196 | 2 |
| #5195 | 2 |
| #5155 | 2 |
| #4563 | 2 |
| #4517 | 2 |
| #4511 | 2 |
| #2212 | 3 |