Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22550488 | C2 | semidirect |
| 3. #22550218 | C2 | semidirect |
| 4. #22550177 | C2 | semidirect |
| 5. #22550082 | C2 | semidirect |
| 7. #22549978 | C2 | semidirect |
| 8. C4×#14523237 | C2 | semidirect |
| 9. #433×C127 | C2 | semidirect |
| 13. #16861209 | C22 | semidirect |
| 15. #16861201 | C22 | semidirect |
| 18. C4×Dic254 | C22 | semidirect |
| 24. #16861143 | C22 | semidirect |
| 25. #16861141 | C22 | semidirect |
| 26. #16861134 | C22 | semidirect |
| 27. #16861134 | C22 | semidirect |
| 31. C4⋊C8×C127 | C22 | semidirect |
| 33. #97×C127 | C22 | semidirect |
| 34. C4×C8×C127 | C22 | semidirect |
| 103. C127 | #3123 | semidirect |
| 112. #433 | D127 | semidirect |
| 130. C4⋊C8 | C2×D127 | semidirect |
| 136. #97 | C2×D127 | semidirect |
| 137. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550488 | 2 |
| #22550350 | 2 |
| #22550218 | 2 |
| #22550177 | 2 |
| #22550082 | 2 |
| #22550029 | 2 |
| #22549978 | 2 |
| C4×#14523237 | 2 |
| #433×C127 | 2 |
| #3123 | 127 |