Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. #5211 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. #4537 | C2 | semidirect |
| 7. C22×C3×D4 | C4 | semidirect |
| 11. C3×#121 | C4 | semidirect |
| 13. C2×C3×C4⋊C4 | C4 | semidirect |
| 18. C3⋊#95 | C22 | semidirect |
| 20. #830 | C22 | semidirect |
| 50. C22×D4 | Dic3 | semidirect |
| 55. #121 | Dic3 | semidirect |
| 57. C2×C4⋊C4 | Dic3 | semidirect |
| 197. C3 | #1510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| #5211 | 2 |
| #5207 | 2 |
| #4537 | 2 |
| #1510 | 3 |