Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 3. #22551590 | C2 | semidirect |
| 5. #22551521 | C2 | semidirect |
| 6. #22551515 | C2 | semidirect |
| 7. #103×C257 | C2 | semidirect |
| 47. Dic257 | SD16 | semidirect |
| 52. C257 | #461 | semidirect |
| 60. #103 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861607 | 2 |
| C2×#16861605 | 2 |
| #22551590 | 2 |
| #22551554 | 2 |
| #22551521 | 2 |
| #22551515 | 2 |
| #103×C257 | 2 |
| #461 | 257 |