Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22550681 | C2 | semidirect |
| 2. #22550317 | C2 | semidirect |
| 3. #22550311 | C2 | semidirect |
| 4. #22550306 | C2 | semidirect |
| 5. C2×#16861152 | C2 | semidirect |
| 6. #22550293 | C2 | semidirect |
| 7. #578×C127 | C2 | semidirect |
| 12. #16861155 | C22 | semidirect |
| 13. #16861153 | C22 | semidirect |
| 14. #16861152 | C22 | semidirect |
| 15. #16861152 | C22 | semidirect |
| 16. #16861150 | C22 | semidirect |
| 17. #16861149 | C22 | semidirect |
| 18. C2×C127⋊C16 | C22 | semidirect |
| 21. #135×C127 | C22 | semidirect |
| 22. C2×Q16×C127 | C22 | semidirect |
| 75. C127 | #3416 | semidirect |
| 76. #578 | D127 | semidirect |
| 88. #135 | C2×D127 | semidirect |
| 89. C2×Q16 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550681 | 2 |
| #22550317 | 2 |
| #22550311 | 2 |
| #22550306 | 2 |
| C2×#16861152 | 2 |
| #22550293 | 2 |
| #578×C127 | 2 |
| #3416 | 127 |