Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16861231 | C2 | semidirect |
| 2. #22550306 | C2 | direct (N × H) |
| 3. C2×#16861155 | C2 | semidirect |
| 4. C2×#16861153 | C2 | semidirect |
| 5. C2×#16861152 | C2 | semidirect |
| 6. C2×#16861150 | C2 | semidirect |
| 7. C22×C127⋊C16 | C2 | semidirect |
| 8. C2×#135×C127 | C2 | semidirect |
| 11. #16861231 | C22 | semidirect |
| 15. #16861155 | C22 | semidirect |
| 16. #16861153 | C22 | semidirect |
| 17. #16861152 | C22 | semidirect |
| 18. #16861150 | C22 | semidirect |
| 21. C2×C127⋊C16 | C22 | semidirect |
| 24. #135×C127 | C22 | semidirect |
| 96. C2×C127 | #508 | semidirect |
| 100. C127 | C2×#508 | semidirect |
| 102. C2×#135 | D127 | semidirect |
| 114. #135 | C2×D127 | semidirect |
| 197. C2 | #22550306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550306 | 2 |
| C2×#16861155 | 2 |
| C2×#16861153 | 2 |
| C2×#16861152 | 2 |
| C2×#16861150 | 2 |
| C22×C127⋊C16 | 2 |
| C2×#135×C127 | 2 |
| C2×#508 | 127 |