Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1840 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 725 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. C23×Dic254 | C2 | semidirect |
| 2. C2×#16861188 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic127 | C2 | semidirect |
| 4. C22×Dic127⋊C4 | C2 | semidirect |
| 8. C22×Dic254 | C22 | semidirect |
| 11. #16861188 | C22 | direct (N × H) |
| 12. C2×C4⋊Dic127 | C22 | semidirect |
| 13. C2×Dic127⋊C4 | C22 | semidirect |
| 21. C2×Dic254 | C23 | semidirect |
| 26. C4⋊Dic127 | C23 | semidirect |
| 27. Dic127⋊C4 | C23 | semidirect |
| 31. C24×C127 | Q8 | semidirect |
| 50. C23×C127 | C2×Q8 | semidirect |
| 62. C22×C127 | C22⋊Q8 | semidirect |
| 65. C22×C127 | C22×Q8 | semidirect |
| 73. C2×C127 | C2×C22⋊Q8 | semidirect |
| 78. C127 | C22×C22⋊Q8 | semidirect |
| 100. C24 | Dic254 | semidirect |
| 123. C23 | C2×Dic254 | semidirect |
| 140. C22 | #16861188 | direct (N × H) |
| 143. C22 | C22×Dic254 | semidirect |
| 151. C2 | C2×#16861188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic254 | 2 |
| C2×#16861188 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×C22⋊Dic127 | 2 |
| C24×C4×C127 | 2 |
| C22×C22⋊Q8 | 127 |