Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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 |
|---|---|---|
| 2. C2×#16861185 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic127 | C2 | semidirect |
| 4. C22×Dic127⋊C4 | C2 | semidirect |
| 6. C23×Q8×C127 | C2 | semidirect |
| 12. #16861185 | C22 | direct (N × H) |
| 13. C2×C4⋊Dic127 | C22 | semidirect |
| 14. C2×Dic127⋊C4 | C22 | semidirect |
| 17. C22×Q8×C127 | C22 | semidirect |
| 22. C23×D127 | Q8 | semidirect |
| 30. C4⋊Dic127 | C23 | semidirect |
| 31. Dic127⋊C4 | C23 | semidirect |
| 35. C2×Q8×C127 | C23 | semidirect |
| 43. C22×D127 | C2×Q8 | semidirect |
| 59. C22×C127 | C22⋊Q8 | semidirect |
| 67. C2×D127 | C22×Q8 | semidirect |
| 72. C2×C127 | C2×C22⋊Q8 | semidirect |
| 78. C127 | C22×C22⋊Q8 | semidirect |
| 79. C23×Q8 | D127 | semidirect |
| 87. C22×Q8 | C2×D127 | semidirect |
| 104. C2×Q8 | C22×D127 | semidirect |
| 141. C22 | #16861185 | direct (N × H) |
| 151. C2 | C2×#16861185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D127 | 2 |
| C2×#16861185 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| C23×Q8×C127 | 2 |
| C22×C22⋊Q8 | 127 |