Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#834 | C2 | semidirect |
| 3. C2×#833 | C2 | semidirect |
| 4. #4539 | C2 | semidirect |
| 5. #4536 | C2 | semidirect |
| 7. C22×C3×D4 | C4 | semidirect |
| 10. C3×#123 | C4 | semidirect |
| 15. C3×#120 | C4 | semidirect |
| 17. C2×C3×C22⋊C4 | C4 | semidirect |
| 30. C24×C3 | C2×C4 | semidirect |
| 45. C22×C3×C4 | C2×C4 | semidirect |
| 55. C3×C22⋊C4 | C2×C4 | semidirect |
| 56. C3×C22⋊C4 | C2×C4 | semidirect |
| 62. C22×D4 | Dic3 | semidirect |
| 66. #123 | Dic3 | semidirect |
| 71. #120 | Dic3 | semidirect |
| 74. C2×C22⋊C4 | Dic3 | semidirect |
| 115. C24 | C2×Dic3 | semidirect |
| 131. C22×C4 | C2×Dic3 | semidirect |
| 145. C22⋊C4 | C2×Dic3 | semidirect |
| 146. C22⋊C4 | C2×Dic3 | semidirect |
| 243. C3 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#534 | 2 |
| C2×#834 | 2 |
| C2×#833 | 2 |
| #4539 | 2 |
| #4536 | 2 |
| #2121 | 3 |