Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 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×#14523248 | C2 | semidirect |
| 2. #22550457 | C2 | direct (N × H) |
| 3. C2×#16861189 | C2 | semidirect |
| 4. C2×#16861184 | C2 | semidirect |
| 5. C2×#16861183 | C2 | semidirect |
| 6. C22×C4⋊C4×C127 | C2 | semidirect |
| 8. C2×#14523248 | C22 | semidirect |
| 14. #16861189 | C22 | semidirect |
| 15. #16861184 | C22 | semidirect |
| 16. #16861183 | C22 | semidirect |
| 22. C2×C4⋊C4×C127 | C22 | semidirect |
| 40. C22×C4×C127 | D4 | semidirect |
| 65. C2×C4×C127 | C2×D4 | semidirect |
| 84. C2×C127 | #537 | semidirect |
| 90. C127 | C2×#537 | semidirect |
| 96. C22×C4⋊C4 | D127 | semidirect |
| 111. C2×C4⋊C4 | C2×D127 | semidirect |
| 128. C22×C4 | D508 | semidirect |
| 155. C2×C4 | C2×D508 | semidirect |
| 175. C2 | #22550457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523248 | 2 |
| #22550457 | 2 |
| C2×#16861189 | 2 |
| C2×#16861184 | 2 |
| C2×#16861183 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#537 | 127 |