Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
800 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 289 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. #22550351 | C2 | semidirect |
| 2. #22549850 | C2 | semidirect |
| 3. C2×#16861124 | C2 | semidirect |
| 6. #16861168 | C22 | semidirect |
| 7. C2×C22⋊Dic127 | C22 | semidirect |
| 8. #16861124 | C22 | semidirect |
| 10. C2×#41×C127 | C4 | semidirect |
| 12. C22×D4×C127 | C4 | semidirect |
| 20. C24×C127 | C2×C4 | semidirect |
| 24. C2×Q8×C127 | C2×C4 | semidirect |
| 28. C2×D4×C127 | C2×C4 | semidirect |
| 29. C2×D4×C127 | C2×C4 | semidirect |
| 32. C22×C4×C127 | C2×C4 | semidirect |
| 33. C22×C4×C127 | C2×C4 | semidirect |
| 72. C127 | #2883 | semidirect |
| 78. C2×#41 | Dic127 | semidirect |
| 80. C22×D4 | Dic127 | semidirect |
| 87. C24 | C2×Dic127 | semidirect |
| 91. C2×Q8 | C2×Dic127 | semidirect |
| 95. C2×D4 | C2×Dic127 | semidirect |
| 96. C2×D4 | C2×Dic127 | semidirect |
| 100. C22×C4 | C2×Dic127 | semidirect |
| 101. C22×C4 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550351 | 2 |
| #22549850 | 2 |
| C2×#16861124 | 2 |
| C2×H(5,𝔽2)×C127 | 2 |
| #2883 | 127 |