Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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. C2×#918 | C2 | semidirect |
| 2. #5727 | C2 | semidirect |
| 4. C3×#494 | C2 | semidirect |
| 5. #5189 | C2 | semidirect |
| 6. #5187 | C2 | semidirect |
| 7. #5186 | C2 | semidirect |
| 8. #5090 | C2 | semidirect |
| 9. #5083 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 46. #494 | D3 | semidirect |
| 92. #204 | D4 | semidirect |
| 204. C3×C4 | #137 | semidirect |
| 260. C4 | #918 | semidirect |
| 263. C3 | #3276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| #5727 | 2 |
| #5726 | 2 |
| C3×#494 | 2 |
| #5189 | 2 |
| #5187 | 2 |
| #5186 | 2 |
| #5090 | 2 |
| #5083 | 2 |
| C4×#204 | 2 |
| #4688 | 2 |
| #3276 | 3 |