Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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×#16861603 | C2 | semidirect |
| 2. C2×C8×D257 | C2 | semidirect |
| 3. #22551567 | C2 | semidirect |
| 4. #22551563 | C2 | semidirect |
| 5. #22551525 | C2 | semidirect |
| 6. #22551514 | C2 | semidirect |
| 7. #102×C257 | C2 | semidirect |
| 31. #14523339 | D4 | semidirect |
| 47. C2×D257 | D8 | semidirect |
| 59. C257 | #466 | semidirect |
| 67. #102 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861603 | 2 |
| C2×C8×D257 | 2 |
| #22551567 | 2 |
| #22551563 | 2 |
| #22551525 | 2 |
| #22551514 | 2 |
| #102×C257 | 2 |
| #466 | 257 |