Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1160 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 3. #11717264 | C2 | direct (N × H) |
| 24. C2×#1039 | Q8 | semidirect |
| 39. #1039 | C2×Q8 | semidirect |
| 51. C2×C52 | C4⋊Q8 | semidirect |
| 70. C52 | C2×C4⋊Q8 | semidirect |
| 88. C2×C5 | #4090 | semidirect |
| 102. C5 | C2×#4090 | semidirect |
| 110. C2 | #11717264 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C22×#6045 | 2 |
| #11717264 | 2 |
| C2×#87806 | 2 |
| C2×C4×#1039 | 2 |
| C2×#4090 | 5 |