Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #22551679 | C2 | direct (N × H) |
| 2. C2×#16861628 | C2 | semidirect |
| 3. C2×#16861627 | C2 | semidirect |
| 4. C2×#16861626 | C2 | semidirect |
| 5. C22×#14523346 | C2 | semidirect |
| 7. #16861628 | C22 | semidirect |
| 8. #16861627 | C22 | semidirect |
| 9. #16861626 | C22 | semidirect |
| 13. C2×#14523346 | C22 | semidirect |
| 46. C2×C257 | #131 | semidirect |
| 49. C257 | C2×#131 | semidirect |
| 97. C2 | #22551679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551679 | 2 |
| C2×#16861628 | 2 |
| C2×#16861627 | 2 |
| C2×#16861626 | 2 |
| C22×#14523346 | 2 |
| C2×#16861617 | 2 |
| C2×#131 | 257 |