Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#16861152 | C2 | semidirect |
| 3. #22549680 | C2 | semidirect |
| 4. C22⋊(C127⋊C16) | C2 | semidirect |
| 5. C22×Q16×C127 | C2 | semidirect |
| 31. Q16×C127 | D4 | semidirect |
| 54. C22×C127 | SD32 | semidirect |
| 70. C127 | #2185 | semidirect |
| 71. C22×Q16 | D127 | semidirect |
| 97. Q16 | C22⋊D127 | semidirect |
| 127. C22 | #16861152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| #22550112 | 2 |
| #22549680 | 2 |
| C22⋊(C127⋊C16) | 2 |
| C22×Q16×C127 | 2 |
| #2185 | 127 |