Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 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. C2×#16861208 | C2 | semidirect |
| 3. #22550154 | C2 | direct (N × H) |
| 4. C2×#16861143 | C2 | semidirect |
| 5. C2×#16861142 | C2 | semidirect |
| 6. C2×Dic127⋊C8 | C2 | semidirect |
| 13. #16861208 | C22 | semidirect |
| 21. #16861143 | C22 | semidirect |
| 22. #16861142 | C22 | semidirect |
| 23. Dic127⋊C8 | C22 | semidirect |
| 50. C2×D4×C127 | Q8 | semidirect |
| 76. D4×C127 | C2×Q8 | semidirect |
| 101. C2×C127 | #474 | semidirect |
| 106. C127 | C2×#474 | semidirect |
| 140. C2×D4 | Dic254 | semidirect |
| 172. D4 | C2×Dic254 | semidirect |
| 207. C2 | #22550154 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861208 | 2 |
| C2×D4×Dic127 | 2 |
| #22550154 | 2 |
| C2×#16861143 | 2 |
| C2×#16861142 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861130 | 2 |
| C2×#102×C127 | 2 |
| C2×#474 | 127 |