Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 8. #4877 | C2 | semidirect |
| 9. #4875 | C2 | semidirect |
| 10. #4857 | C2 | semidirect |
| 11. #4854 | C2 | semidirect |
| 64. C2×Dic6 | Q8 | semidirect |
| 254. C3 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| C2×#887 | 2 |
| C3×#428 | 2 |
| #5120 | 2 |
| #5118 | 2 |
| #5004 | 2 |
| #4964 | 2 |
| #4877 | 2 |
| #4875 | 2 |
| #4857 | 2 |
| #4854 | 2 |
| #3078 | 3 |