Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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. #4997 | C2 | semidirect |
| 5. #4533 | C2 | semidirect |
| 11. C2×#208 | C4 | semidirect |
| 14. C22×C3⋊C8 | C4 | semidirect |
| 17. #836 | C4 | semidirect |
| 18. #833 | C4 | semidirect |
| 144. C3 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#948 | 2 |
| C3×#410 | 2 |
| #5237 | 2 |
| #4997 | 2 |
| #4533 | 2 |
| #1757 | 3 |