Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 4. C2×#822 | C2 | direct (N × H) |
| 16. #822 | C22 | direct (N × H) |
| 82. C22×C3 | #108 | semidirect |
| 108. C2×C3 | C2×#108 | semidirect |
| 112. C22 | #822 | direct (N × H) |
| 120. C3 | C22×#108 | semidirect |
| 123. C2 | C2×#822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C22×#208 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#822 | 2 |
| C22×#108 | 3 |