Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C23×C3×C8 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 15. #930 | C4 | semidirect |
| 21. C23×C8 | D3 | semidirect |
| 46. C2×C3×C8 | D4 | semidirect |
| 118. C2×C8 | #67 | semidirect |
| 129. C22×C3 | #102 | semidirect |
| 193. C22 | #821 | semidirect |
| 205. C3 | #1893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C8 | 2 |
| C2×#930 | 2 |
| #5212 | 2 |
| C2×#821 | 2 |
| #4551 | 2 |
| #1893 | 3 |