Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
136 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 11. #812 | C4 | semidirect |
| 15. C2×C3⋊C16 | C4 | semidirect |
| 108. C3 | #1379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#405 | 2 |
| C2×#812 | 2 |
| C22×C3⋊C16 | 2 |
| #1379 | 3 |