Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 71 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×Q8×C25 | C2 | semidirect |
| 2. C2×#87724 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 5. C22⋊#6014 | C2 | semidirect |
| 22. Q8×C25 | D4 | semidirect |
| 39. C22×C25 | SD16 | semidirect |
| 79. C22×Q8 | D25 | semidirect |
| 84. C25 | #448 | semidirect |
| 116. Q8 | C22⋊D25 | semidirect |
| 132. C22 | #87724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| C2×#87724 | 2 |
| #11716492 | 2 |
| #11716384 | 2 |
| C22⋊#6014 | 2 |
| #65516 | 5 |