Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. C3×#410 | C2 | semidirect |
| 3. #5236 | C2 | semidirect |
| 4. #5006 | C2 | semidirect |
| 5. #5005 | C2 | semidirect |
| 6. #4998 | C2 | semidirect |
| 7. #4997 | C2 | semidirect |
| 17. C2×#216 | C4 | semidirect |
| 18. C2×#215 | C4 | semidirect |
| 19. C2×#214 | C4 | semidirect |
| 20. C2×#213 | C4 | semidirect |
| 37. #410 | D3 | semidirect |
| 258. C3 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#950 | 2 |
| C3×#410 | 2 |
| #5236 | 2 |
| #5006 | 2 |
| #5005 | 2 |
| #4998 | 2 |
| #4997 | 2 |
| #1976 | 3 |