Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 77. Dic254 | Q16 | semidirect |
| 113. C127 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550606 | 2 |
| #22550601 | 2 |
| #22550225 | 2 |
| #22550169 | 2 |
| #22550168 | 2 |
| #22550085 | 2 |
| #22550083 | 2 |
| C8×Dic254 | 2 |
| C4×Dic508 | 2 |
| #22549968 | 2 |
| #487×C127 | 2 |
| #3363 | 127 |