Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
342 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×#6034 | C2 | semidirect |
| 2. C2×#87863 | C2 | semidirect |
| 4. C22⋊#6034 | C2 | semidirect |
| 5. #11716896 | C2 | semidirect |
| 6. #11716895 | C2 | semidirect |
| 7. C4⋊#6034 | C2 | semidirect |
| 37. #6034 | D4 | semidirect |
| 48. C22×C52 | M16 | semidirect |
| 120. C52 | #435 | semidirect |
| 127. C22×C5 | #700 | semidirect |
| 187. C5 | #65693 | semidirect |
| 193. C22 | #87863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C2×#87863 | 2 |
| #11717201 | 2 |
| C22⋊#6034 | 2 |
| #11716896 | 2 |
| #11716895 | 2 |
| C4⋊#6034 | 2 |
| #65693 | 5 |