Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 2. C2×#836 | C2 | semidirect |
| 78. C22×C3 | #101 | semidirect |
| 108. C22 | #836 | semidirect |
| 114. C3 | #1784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C2×#836 | 2 |
| #5207 | 2 |
| #1784 | 3 |