Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 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 |
|---|---|---|
| 2. C4⋊C4×D257 | C2 | semidirect |
| 3. #22551525 | C2 | semidirect |
| 4. #22551514 | C2 | semidirect |
| 5. #22551512 | C2 | semidirect |
| 6. #22551504 | C2 | semidirect |
| 7. #107×C257 | C2 | semidirect |
| 52. C257 | #480 | semidirect |
| 57. #107 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22551567 | 2 |
| C4⋊C4×D257 | 2 |
| #22551525 | 2 |
| #22551514 | 2 |
| #22551512 | 2 |
| #22551504 | 2 |
| #107×C257 | 2 |
| #480 | 257 |