Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5825 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. C22×#214 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5042 | C2 | semidirect |
| 7. #5041 | C2 | semidirect |
| 8. #5004 | C2 | semidirect |
| 9. #4998 | C2 | semidirect |
| 27. #924 | C22 | semidirect |
| 29. C2×#208 | C22 | semidirect |
| 31. C22×C3⋊C8 | C22 | semidirect |
| 33. #810 | C22 | semidirect |
| 34. #808 | C22 | semidirect |
| 35. #807 | C22 | semidirect |
| 77. C2×C3⋊C8 | D4 | semidirect |
| 235. C3 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5825 | 2 |
| C2×#948 | 2 |
| C22×#214 | 2 |
| #5215 | 2 |
| #5042 | 2 |
| #5041 | 2 |
| #5004 | 2 |
| #4998 | 2 |
| #3057 | 3 |