Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×Q16×C25 | C2 | semidirect |
| 3. #11716506 | C2 | semidirect |
| 5. C2×#87723 | C2 | semidirect |
| 7. #11716364 | C2 | semidirect |
| 88. C2×Q16 | D25 | semidirect |
| 94. C25 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C25 | 2 |
| #11716509 | 2 |
| #11716506 | 2 |
| C2×#87724 | 2 |
| C2×#87723 | 2 |
| C2×#87713 | 2 |
| #11716364 | 2 |
| #65479 | 5 |