Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
704 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
|---|---|---|
| 6. #11716956 | C2 | direct (N × H) |
| 12. C2×#6039 | C4 | semidirect |
| 23. C2×#1039 | Q8 | semidirect |
| 30. #6039 | C2×C4 | semidirect |
| 46. #1039 | C2×Q8 | semidirect |
| 69. C2×C52 | C4×Q8 | semidirect |
| 102. C52 | C2×C4×Q8 | semidirect |
| 136. C2×C5 | #4033 | semidirect |
| 153. C5 | C2×#4033 | semidirect |
| 163. C2 | #11716956 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C2×C4×#1039 | 2 |
| C2×C5×#683 | 2 |
| C2×#87781 | 2 |
| C2×Dic52 | 2 |
| #11716956 | 2 |
| C2×#4033 | 5 |