Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
177 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #11716412 | C2 | semidirect |
| 5. #11716411 | C2 | semidirect |
| 14. M16×C25 | C4 | semidirect |
| 15. #87716 | C4 | semidirect |
| 16. #87712 | C4 | semidirect |
| 30. C8×C25 | C2×C4 | semidirect |
| 31. #6014 | C2×C4 | semidirect |
| 85. C25 | #428 | semidirect |
| 102. M16 | #1035 | semidirect |
| 127. C8 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716549 | 2 |
| C2×C4⋊#1035 | 2 |
| M16×D25 | 2 |
| #11716412 | 2 |
| #11716411 | 2 |
| #65727 | 5 |