Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1624 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1624 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 |
|---|---|---|
| 2. C2×#16861207 | C2 | direct (N × H) |
| 10. #16861207 | C22 | direct (N × H) |
| 20. C22×Dic127 | Q8 | semidirect |
| 34. C2×Dic127 | C2×Q8 | semidirect |
| 45. C22×C127 | C4⋊Q8 | semidirect |
| 52. Dic127 | C22×Q8 | semidirect |
| 53. C2×C127 | C2×C4⋊Q8 | semidirect |
| 57. C127 | C22×C4⋊Q8 | semidirect |
| 102. C22 | #16861207 | direct (N × H) |
| 110. C2 | C2×#16861207 | 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×#16861207 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×C4×Dic127 | 2 |
| C23×Q8×C127 | 2 |
| C22×C4⋊Q8 | 127 |