Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22549831 | C2 | semidirect |
| 5. #22549648 | C2 | semidirect |
| 6. #22549646 | C2 | semidirect |
| 7. #405×C127 | C2 | semidirect |
| 15. C2×#14523231 | C4 | semidirect |
| 16. C2×C8×D127 | C4 | semidirect |
| 18. #16861127 | C4 | semidirect |
| 19. #16861125 | C4 | semidirect |
| 107. C127 | #1757 | semidirect |
| 112. #405 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861215 | 2 |
| #22549858 | 2 |
| #22549849 | 2 |
| #22549831 | 2 |
| #22549648 | 2 |
| #22549646 | 2 |
| #405×C127 | 2 |
| #1757 | 127 |