Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
208 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #22549598 | C2 | semidirect |
| 5. #22549597 | C2 | semidirect |
| 6. #22549597 | C2 | semidirect |
| 7. #322×C127 | C2 | semidirect |
| 51. C8×C127 | M16 | semidirect |
| 67. C127 | #1451 | semidirect |
| 74. #322 | D127 | semidirect |
| 118. C8 | #14523231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549927 | 2 |
| C4×#14523231 | 2 |
| C4×C8×D127 | 2 |
| #22549598 | 2 |
| #22549597 | 2 |
| #322×C127 | 2 |
| #1451 | 127 |