Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 80. C52 | #479 | semidirect |
| 115. C5 | #65166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717210 | 2 |
| #11717207 | 2 |
| C52×#107 | 2 |
| #11716683 | 2 |
| #11716681 | 2 |
| #11716677 | 2 |
| #11716675 | 2 |
| #65166 | 5 |