Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 29. #6045 | Q8 | semidirect |
| 82. C52 | #475 | semidirect |
| 118. C5 | #65143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717208 | 2 |
| #11717207 | 2 |
| C52×#106 | 2 |
| #11716683 | 2 |
| #11716681 | 2 |
| #11716677 | 2 |
| #11716675 | 2 |
| #65143 | 5 |