Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 20. #808 | C4 | semidirect |
| 21. #807 | C4 | semidirect |
| 22. #803 | C4 | semidirect |
| 95. C3⋊C8 | C42 | semidirect |
| 189. C3 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊C4 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| C4×C4⋊Dic3 | 2 |
| C2×#803 | 2 |
| #4529 | 2 |
| #1776 | 3 |