Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22550693 | C2 | semidirect |
| 2. #22550314 | C2 | semidirect |
| 3. C2×#16861154 | C2 | semidirect |
| 4. #22550146 | C2 | semidirect |
| 5. #22549693 | C2 | semidirect |
| 6. #22549684 | C2 | semidirect |
| 7. #350×C127 | C2 | semidirect |
| 91. C127 | #2193 | semidirect |
| 98. #350 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550693 | 2 |
| #22550314 | 2 |
| C2×#16861154 | 2 |
| #22550146 | 2 |
| #22549693 | 2 |
| #22549684 | 2 |
| #350×C127 | 2 |
| #2193 | 127 |