Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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. C22×C4⋊Dic3 | C2 | semidirect |
| 3. C23×C3⋊C8 | C2 | semidirect |
| 4. C2×#832 | C2 | direct (N × H) |
| 9. C22×C3×D4 | C4 | semidirect |
| 14. C2×C4⋊Dic3 | C22 | semidirect |
| 16. C22×C3⋊C8 | C22 | semidirect |
| 17. #832 | C22 | direct (N × H) |
| 30. C2×C3×D4 | C2×C4 | semidirect |
| 39. C4⋊Dic3 | C23 | semidirect |
| 41. C2×C3⋊C8 | C23 | semidirect |
| 45. C22×D4 | Dic3 | semidirect |
| 65. C3×D4 | C22×C4 | semidirect |
| 82. C2×D4 | C2×Dic3 | semidirect |
| 98. C22×C3 | #102 | semidirect |
| 118. D4 | C22×Dic3 | semidirect |
| 128. C2×C3 | C2×#102 | semidirect |
| 136. C22 | #832 | direct (N × H) |
| 145. C3 | C22×#102 | semidirect |
| 147. C2 | C2×#832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#832 | 2 |
| C22×#102 | 3 |