Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
738 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 289 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. #22550643 | C2 | semidirect |
| 2. #41×Dic127 | C2 | semidirect |
| 3. #22549893 | C2 | semidirect |
| 4. C2×#16861136 | C2 | semidirect |
| 7. C2×#14523232 | C22 | semidirect |
| 10. #16861168 | C22 | semidirect |
| 11. C2×C4×Dic127 | C22 | semidirect |
| 12. #16861136 | C22 | semidirect |
| 13. #16861136 | C22 | semidirect |
| 15. 2−1+4×C127 | C4 | semidirect |
| 17. H(5,𝔽2)×C127 | C4 | semidirect |
| 35. #41×C127 | C2×C4 | semidirect |
| 39. C2×Q8×C127 | C2×C4 | semidirect |
| 43. C2×D4×C127 | C2×C4 | semidirect |
| 84. C127 | #2901 | semidirect |
| 91. 2−1+4 | Dic127 | semidirect |
| 93. H(5,𝔽2) | Dic127 | semidirect |
| 110. #41 | C2×Dic127 | semidirect |
| 114. C2×Q8 | C2×Dic127 | semidirect |
| 118. C2×D4 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550643 | 2 |
| #41×Dic127 | 2 |
| #22549893 | 2 |
| C2×#16861136 | 2 |
| #585×C127 | 2 |
| #2901 | 127 |