Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22550426 | C2 | semidirect |
| 2. #22550189 | C2 | semidirect |
| 3. #22550156 | C2 | semidirect |
| 4. #22550071 | C2 | semidirect |
| 5. #22550010 | C2 | semidirect |
| 6. C4×#14523233 | C2 | semidirect |
| 7. #22549929 | C2 | semidirect |
| 8. C2×C4×D4×C127 | C2 | semidirect |
| 11. #16861209 | C22 | semidirect |
| 12. #16861206 | C22 | semidirect |
| 17. C4×D508 | C22 | semidirect |
| 18. #16861142 | C22 | semidirect |
| 19. C4⋊(C127⋊C8) | C22 | semidirect |
| 21. #16861129 | C22 | semidirect |
| 23. C4×C127⋊C8 | C22 | semidirect |
| 81. D4×C127 | #41 | semidirect |
| 88. C2×C4×C127 | D8 | semidirect |
| 121. C127 | #3100 | semidirect |
| 123. C2×C4×D4 | D127 | semidirect |
| 199. D4 | #14523248 | semidirect |
| 208. C2×C4 | #14523233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| #22550189 | 2 |
| #22550156 | 2 |
| #22550071 | 2 |
| #22550010 | 2 |
| C4×#14523233 | 2 |
| #22549929 | 2 |
| C2×C4×D4×C127 | 2 |
| #3100 | 127 |