Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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. C22×C3⋊C16 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4491 | C2 | semidirect |
| 7. #4490 | C2 | semidirect |
| 24. #467 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 99. C22×C3 | SD32 | semidirect |
| 137. C22 | #828 | semidirect |
| 145. C3 | #2217 | 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 |
| C22×C3⋊C16 | 2 |
| #4564 | 2 |
| #4491 | 2 |
| #4490 | 2 |
| #2217 | 3 |