Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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×#16861606 | C2 | semidirect |
| 2. C2×#16861601 | C2 | semidirect |
| 3. #22551572 | C2 | semidirect |
| 5. #22551525 | C2 | semidirect |
| 6. #22551517 | C2 | semidirect |
| 7. #102×C257 | C2 | semidirect |
| 30. #14523339 | D4 | semidirect |
| 55. C257 | #468 | semidirect |
| 63. #102 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861606 | 2 |
| C2×#16861601 | 2 |
| #22551572 | 2 |
| #22551563 | 2 |
| #22551525 | 2 |
| #22551517 | 2 |
| #102×C257 | 2 |
| #468 | 257 |