Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 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. C23×C3⋊C8 | C2 | semidirect |
| 3. C2×#830 | C2 | direct (N × H) |
| 12. C22×C3⋊C8 | C22 | semidirect |
| 13. #830 | C22 | direct (N × H) |
| 19. C24×C3 | C8 | semidirect |
| 32. C2×C3⋊C8 | C23 | semidirect |
| 47. C23×C3 | C2×C8 | semidirect |
| 62. C24 | C3⋊C8 | semidirect |
| 79. C22×C3 | C22⋊C8 | semidirect |
| 82. C22×C3 | C22×C8 | semidirect |
| 92. C23 | C2×C3⋊C8 | semidirect |
| 107. C2×C3 | C2×C22⋊C8 | semidirect |
| 114. C22 | #830 | direct (N × H) |
| 116. C22 | C22×C3⋊C8 | semidirect |
| 123. C3 | C22×C22⋊C8 | semidirect |
| 125. C2 | C2×#830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#830 | 2 |
| C22×C22⋊C8 | 3 |