Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22550163 | C2 | semidirect |
| 3. C8×D508 | C2 | semidirect |
| 4. #22549627 | C2 | semidirect |
| 5. #22549625 | C2 | semidirect |
| 6. #22549620 | C2 | semidirect |
| 7. #486×C127 | C2 | semidirect |
| 83. C127 | #1677 | semidirect |
| 84. #486 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550163 | 2 |
| #22550068 | 2 |
| C8×D508 | 2 |
| #22549627 | 2 |
| #22549625 | 2 |
| #22549620 | 2 |
| #486×C127 | 2 |
| #1677 | 127 |