Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
265 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 83 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×#6032 | C2 | semidirect |
| 2. C2×#87849 | C2 | semidirect |
| 4. C22⋊#6032 | C2 | semidirect |
| 5. #11716846 | C2 | semidirect |
| 6. #11716845 | C2 | semidirect |
| 7. C4⋊#6032 | C2 | semidirect |
| 38. #6032 | D4 | semidirect |
| 55. C22×C52 | M16 | semidirect |
| 141. C52 | #435 | semidirect |
| 153. C22×C5 | #681 | semidirect |
| 154. C22×C5 | #700 | semidirect |
| 218. C5 | #65300 | semidirect |
| 219. C5 | #65693 | semidirect |
| 225. C22 | #87849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6032 | 2 |
| C2×#87849 | 2 |
| C5×#4027 | 2 |
| C22⋊#6032 | 2 |
| #11716846 | 2 |
| #11716845 | 2 |
| C4⋊#6032 | 2 |
| #65693 | 5 |
| #65300 | 5 |