Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23762284 | C2 | semidirect |
| 3. #23761360 | C2 | semidirect |
| 4. #23761316 | C2 | semidirect |
| 5. C79×#1372 | C2 | semidirect |
| 45. C16×C79 | M16 | semidirect |
| 77. #1372 | D79 | semidirect |
| 80. C79 | #12086 | semidirect |
| 120. C16 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1264 | 2 |
| #23762284 | 2 |
| #23761360 | 2 |
| #23761316 | 2 |
| C79×#1372 | 2 |
| #12086 | 79 |