Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×C3×#108 | C2 | semidirect |
| 4. #5122 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 18. #821 | C4 | semidirect |
| 19. #821 | C4 | semidirect |
| 22. #816 | C4 | semidirect |
| 23. #816 | C4 | semidirect |
| 26. C2×#108 | D3 | semidirect |
| 204. C3 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#108 | 2 |
| C2×#825 | 2 |
| #5129 | 2 |
| #5122 | 2 |
| #5113 | 2 |
| #4555 | 2 |
| #4550 | 2 |
| #1929 | 3 |