Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×#16861601 | C2 | semidirect |
| 2. C22×#14523339 | C2 | semidirect |
| 4. #22551521 | C2 | semidirect |
| 5. #22551504 | C2 | semidirect |
| 6. #22551502 | C2 | semidirect |
| 7. C22⋊C8×C257 | C2 | semidirect |
| 29. #14523339 | D4 | semidirect |
| 39. C22×C257 | M16 | semidirect |
| 55. C257 | #435 | semidirect |
| 62. C22⋊C8 | D257 | semidirect |
| 98. C22 | #16861601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861601 | 2 |
| C22×#14523339 | 2 |
| C4×C22⋊D257 | 2 |
| #22551521 | 2 |
| #22551504 | 2 |
| #22551502 | 2 |
| C22⋊C8×C257 | 2 |
| #435 | 257 |