Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
282 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 43. C2×C3×C8 | Q8 | semidirect |
| 47. C3×C4⋊C4 | Q8 | semidirect |
| 58. C2×C3⋊C8 | Q8 | semidirect |
| 117. C2×C8 | Dic6 | semidirect |
| 126. C4⋊C4 | Dic6 | semidirect |
| 199. C3 | #2058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| C2×#817 | 2 |
| #4984 | 2 |
| C2×#808 | 2 |
| C3×#340 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #2058 | 3 |