Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#904 | C2 | semidirect |
| 2. #5553 | C2 | semidirect |
| 3. #5551 | C2 | semidirect |
| 4. C3×C8×D4 | C2 | semidirect |
| 5. #5114 | C2 | semidirect |
| 6. #4849 | C2 | semidirect |
| 7. #4843 | C2 | semidirect |
| 8. #4734 | C2 | semidirect |
| 9. #4733 | C2 | semidirect |
| 10. #4693 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 53. C8×D4 | D3 | semidirect |
| 93. #204 | D4 | semidirect |
| 209. C3×C4 | #135 | semidirect |
| 271. C4 | #904 | semidirect |
| 274. C3 | #3284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5553 | 2 |
| #5551 | 2 |
| C3×C8×D4 | 2 |
| #5114 | 2 |
| #4849 | 2 |
| #4843 | 2 |
| #4734 | 2 |
| #4733 | 2 |
| #4693 | 2 |
| C4×#204 | 2 |
| #3284 | 3 |