Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
592 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#87812 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 38. C22×C52 | Q16 | semidirect |
| 79. C52 | #451 | semidirect |
| 82. C22×C5 | #689 | semidirect |
| 117. C5 | #65339 | semidirect |
| 120. C22 | #87812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C52×C22⋊Q8 | 2 |
| C2×#87812 | 2 |
| C22⋊#6029 | 2 |
| #11716677 | 2 |
| #65339 | 5 |