Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23762155 | C2 | semidirect |
| 4. #23762081 | C2 | semidirect |
| 6. M16×C79⋊C8 | C2 | semidirect |
| 7. C79×#1997 | C2 | semidirect |
| 89. M16×C79 | SD16 | semidirect |
| 131. C79⋊C8 | #100 | semidirect |
| 155. #1997 | D79 | semidirect |
| 161. C79 | #9793 | semidirect |
| 238. M16 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098937 | 2 |
| #23764240 | 2 |
| #23762155 | 2 |
| #23762081 | 2 |
| #23762069 | 2 |
| M16×C79⋊C8 | 2 |
| C79×#1997 | 2 |
| #9793 | 79 |