Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 71. #216 | Q8 | semidirect |
| 215. C3 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5567 | 2 |
| #5094 | 2 |
| #5078 | 2 |
| #5065 | 2 |
| #5063 | 2 |
| C4×#216 | 2 |
| Q8×C3⋊C8 | 2 |
| #5022 | 2 |
| #5020 | 2 |
| #3383 | 3 |