Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. C2×C3×#108 | C2 | semidirect |
| 4. #5121 | C2 | semidirect |
| 6. #5102 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 24. C2×#108 | D3 | semidirect |
| 188. C3 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#108 | 2 |
| #5131 | 2 |
| C2×#823 | 2 |
| #5121 | 2 |
| C2×#821 | 2 |
| #5102 | 2 |
| #4554 | 2 |
| #2063 | 3 |