Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #22550114 | C2 | direct (N × H) |
| 4. C2×#16861143 | C2 | semidirect |
| 5. C2×#16861133 | C2 | semidirect |
| 6. C22×Q16×C127 | C2 | semidirect |
| 16. #16861143 | C22 | semidirect |
| 17. #16861133 | C22 | semidirect |
| 20. C2×Q16×C127 | C22 | semidirect |
| 47. C22×D127 | Q16 | semidirect |
| 75. C2×D127 | C2×Q16 | semidirect |
| 82. C2×C127 | #467 | semidirect |
| 88. C127 | C2×#467 | semidirect |
| 89. C22×Q16 | D127 | semidirect |
| 98. C2×Q16 | C2×D127 | semidirect |
| 171. C2 | #22550114 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D127 | 2 |
| C2×#16861185 | 2 |
| #22550114 | 2 |
| C2×#16861143 | 2 |
| C2×#16861133 | 2 |
| C22×Q16×C127 | 2 |
| C2×#467 | 127 |