Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 632 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 |
|---|---|---|
| 1. C22×#6045 | C2 | semidirect |
| 3. C2×#87810 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 30. #6045 | D4 | semidirect |
| 42. C22×C52 | SD16 | semidirect |
| 84. C52 | #448 | semidirect |
| 90. C22×C5 | #687 | semidirect |
| 126. C5 | #65329 | semidirect |
| 132. C22 | #87810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C52×#121 | 2 |
| C2×#87810 | 2 |
| C22⋊#6029 | 2 |
| #11716677 | 2 |
| #65329 | 5 |