Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #23764389 | C2 | semidirect |
| 4. #23762156 | C2 | semidirect |
| 5. #23762080 | C2 | semidirect |
| 7. C8×M16×C79 | C2 | semidirect |
| 90. M16×C79 | SD16 | semidirect |
| 129. C8×C79 | #100 | semidirect |
| 160. C8×M16 | D79 | semidirect |
| 161. C79 | #9793 | semidirect |
| 238. M16 | #11929613 | semidirect |
| 285. C8 | #14579077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098936 | 2 |
| #23764389 | 2 |
| #23764240 | 2 |
| #23762156 | 2 |
| #23762080 | 2 |
| #23762067 | 2 |
| C8×M16×C79 | 2 |
| #9793 | 79 |