Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 48. C3×Q16 | Q8 | semidirect |
| 114. Q16 | Dic6 | semidirect |
| 177. C3 | #3390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5569 | 2 |
| C3×C4×Q16 | 2 |
| #5184 | 2 |
| #5022 | 2 |
| #4876 | 2 |
| #4796 | 2 |
| #4793 | 2 |
| #4683 | 2 |
| #4679 | 2 |
| #3390 | 3 |