Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C22×#14523238 | C2 | semidirect |
| 4. #22550098 | C2 | direct (N × H) |
| 5. C2×C4⋊(C127⋊C8) | C2 | semidirect |
| 6. C2×#16861132 | C2 | semidirect |
| 8. C2×C4×Q8×C127 | C2 | semidirect |
| 12. C2×#14523238 | C22 | semidirect |
| 21. C4⋊(C127⋊C8) | C22 | semidirect |
| 22. #16861132 | C22 | semidirect |
| 26. C4×Q8×C127 | C22 | semidirect |
| 110. C2×C127 | #464 | semidirect |
| 116. C127 | C2×#464 | semidirect |
| 120. C2×C4×Q8 | D127 | semidirect |
| 137. C4×Q8 | C2×D127 | semidirect |
| 227. C2 | #22550098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523238 | 2 |
| C22×#14523235 | 2 |
| C2×#16861197 | 2 |
| #22550098 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| C2×#16861132 | 2 |
| C2×#16861129 | 2 |
| C2×C4×Q8×C127 | 2 |
| C2×#464 | 127 |