Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#870 | C2 | semidirect |
| 4. #5022 | C2 | semidirect |
| 5. #5009 | C2 | semidirect |
| 6. #4995 | C2 | semidirect |
| 7. #4924 | C2 | semidirect |
| 176. C3 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| C2×#870 | 2 |
| #5232 | 2 |
| #5022 | 2 |
| #5009 | 2 |
| #4995 | 2 |
| #4924 | 2 |
| #3080 | 3 |