Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
736 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 3. C2×#836 | C2 | direct (N × H) |
| 14. #836 | C22 | direct (N × H) |
| 80. C22×C3 | #101 | semidirect |
| 105. C2×C3 | C2×#101 | semidirect |
| 109. C22 | #836 | direct (N × H) |
| 116. C3 | C22×#101 | semidirect |
| 119. C2 | C2×#836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C22×#208 | 2 |
| C2×#836 | 2 |
| C22×#101 | 3 |