Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #4527 | C2 | semidirect |
| 5. #4526 | C2 | semidirect |
| 9. C2×#217 | C4 | semidirect |
| 15. #926 | C4 | semidirect |
| 173. C3 | #1828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5798 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| #4527 | 2 |
| #4526 | 2 |
| #1828 | 3 |