Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5516 | C2 | semidirect |
| 5. #5004 | C2 | semidirect |
| 6. #4533 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 15. C2×#216 | C4 | semidirect |
| 16. C2×#214 | C4 | semidirect |
| 213. C3 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#951 | 2 |
| #5516 | 2 |
| C3×#410 | 2 |
| #5236 | 2 |
| #5004 | 2 |
| #4533 | 2 |
| #4531 | 2 |
| #1905 | 3 |