Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 2. C22×#6045 | C2 | semidirect |
| 3. C2×C52×M16 | C2 | semidirect |
| 4. #11717229 | C2 | direct (N × H) |
| 5. C2×#87802 | C2 | semidirect |
| 6. C2×#87800 | C2 | semidirect |
| 18. C2×#6045 | C22 | semidirect |
| 19. C52×M16 | C22 | semidirect |
| 21. #87802 | C22 | semidirect |
| 22. #87800 | C22 | semidirect |
| 45. C2×C5×M16 | D5 | semidirect |
| 71. C5×M16 | C2×D5 | semidirect |
| 77. C2×C52 | #137 | semidirect |
| 104. C2×M16 | C5⋊D5 | semidirect |
| 105. C52 | C2×#137 | semidirect |
| 130. M16 | C2×C5⋊D5 | semidirect |
| 133. C2×C5 | #4055 | semidirect |
| 155. C5 | C2×#4055 | semidirect |
| 168. C2 | #11717229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C22×#6045 | 2 |
| C2×C52×M16 | 2 |
| #11717229 | 2 |
| C2×#87802 | 2 |
| C2×#87800 | 2 |
| C2×#4055 | 5 |