Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 17. C3×#97 | C4 | semidirect |
| 21. C4⋊(C3⋊C8) | C4 | semidirect |
| 63. #97 | Dic3 | semidirect |
| 84. C3×C8 | C4⋊C4 | semidirect |
| 144. C8 | C4⋊Dic3 | semidirect |
| 163. C3 | #1771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#97 | 2 |
| C2×#815 | 2 |
| C2×C8×Dic3 | 2 |
| C4×C4⋊Dic3 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4550 | 2 |
| #1771 | 3 |