Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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. C22×#14523249 | C2 | semidirect |
| 2. #22550427 | C2 | direct (N × H) |
| 3. C2×#16861206 | C2 | semidirect |
| 4. C2×#16861198 | C2 | semidirect |
| 5. C2×#16861184 | C2 | semidirect |
| 6. C2×#16861171 | C2 | semidirect |
| 7. C2×C42×D127 | C2 | semidirect |
| 8. C2×C4⋊Q8×C127 | C2 | semidirect |
| 10. C2×#14523249 | C22 | semidirect |
| 17. #16861206 | C22 | semidirect |
| 18. #16861198 | C22 | semidirect |
| 19. #16861184 | C22 | semidirect |
| 20. #16861171 | C22 | semidirect |
| 24. C42×D127 | C22 | semidirect |
| 26. C4⋊Q8×C127 | C22 | semidirect |
| 42. C2×C4×D127 | D4 | semidirect |
| 71. C4×D127 | C2×D4 | semidirect |
| 76. C2×C4×C127 | #41 | semidirect |
| 91. C4×C127 | C2×#41 | semidirect |
| 94. C2×C127 | #532 | semidirect |
| 100. C127 | C2×#532 | semidirect |
| 103. C2×C4⋊Q8 | D127 | semidirect |
| 118. C4⋊Q8 | C2×D127 | semidirect |
| 176. C2×C4 | #14523249 | semidirect |
| 193. C4 | C2×#14523249 | semidirect |
| 196. C2 | #22550427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523249 | 2 |
| #22550427 | 2 |
| C2×#16861206 | 2 |
| C2×#16861198 | 2 |
| C2×#16861184 | 2 |
| C2×#16861171 | 2 |
| C2×C42×D127 | 2 |
| C2×C4⋊Q8×C127 | 2 |
| C2×#532 | 127 |