Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22550601 | C2 | semidirect |
| 4. #22550181 | C2 | semidirect |
| 7. #22550083 | C2 | semidirect |
| 8. C8×Dic254 | C2 | semidirect |
| 9. #22549968 | C2 | semidirect |
| 11. #487×C127 | C2 | semidirect |
| 116. C127 | #3364 | semidirect |
| 120. #487 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550601 | 2 |
| #22550600 | 2 |
| #22550232 | 2 |
| #22550181 | 2 |
| #22550153 | 2 |
| #22550101 | 2 |
| #22550083 | 2 |
| C8×Dic254 | 2 |
| #22549968 | 2 |
| C4×#14523237 | 2 |
| #487×C127 | 2 |
| #3364 | 127 |