Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. C3×#467 | C2 | semidirect |
| 2. C2×#828 | C2 | semidirect |
| 4. C2×#812 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4491 | C2 | semidirect |
| 7. #4489 | C2 | semidirect |
| 24. #467 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 145. C3 | #2220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#467 | 2 |
| C2×#828 | 2 |
| #5115 | 2 |
| C2×#812 | 2 |
| #4564 | 2 |
| #4491 | 2 |
| #4489 | 2 |
| #2220 | 3 |