Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
180 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#87721 | C2 | semidirect |
| 3. #11716486 | C2 | semidirect |
| 4. C2×#87716 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 6. #11716357 | C2 | semidirect |
| 7. #11716355 | C2 | semidirect |
| 37. #6014 | D4 | semidirect |
| 100. C25 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#121 | 2 |
| C2×#87721 | 2 |
| #11716486 | 2 |
| C2×#87716 | 2 |
| #11716381 | 2 |
| #11716357 | 2 |
| #11716355 | 2 |
| #65331 | 5 |