Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22550280 | C2 | direct (N × H) |
| 25. C2×C127⋊C8 | Q8 | semidirect |
| 34. C2×C8×C127 | Q8 | semidirect |
| 45. C127⋊C8 | C2×Q8 | semidirect |
| 53. C8×C127 | C2×Q8 | semidirect |
| 65. C2×C127 | #500 | semidirect |
| 70. C127 | C2×#500 | semidirect |
| 99. C2×C8 | Dic254 | semidirect |
| 123. C8 | C2×Dic254 | semidirect |
| 135. C2 | #22550280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861208 | 2 |
| #22550280 | 2 |
| C2×#16861143 | 2 |
| C2×#16861142 | 2 |
| C2×C8×Dic127 | 2 |
| C2×#107×C127 | 2 |
| C2×#500 | 127 |