Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. C2×#87802 | C2 | semidirect |
| 4. #11716685 | C2 | semidirect |
| 5. #11716683 | C2 | semidirect |
| 34. C22×C52 | Q16 | semidirect |
| 71. C52 | #467 | semidirect |
| 74. C22×C5 | Dic20 | semidirect |
| 105. C5 | #65405 | semidirect |
| 108. C22 | #87802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| #11717244 | 2 |
| C2×#87802 | 2 |
| #11716685 | 2 |
| #11716683 | 2 |
| #65405 | 5 |