Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765197 | C2 | semidirect |
| 3. #23762157 | C2 | semidirect |
| 4. #23761364 | C2 | semidirect |
| 5. #23761362 | C2 | semidirect |
| 6. #23761360 | C2 | semidirect |
| 7. C79×#1332 | C2 | semidirect |
| 74. D632 | M16 | semidirect |
| 95. Q16×C79 | M16 | semidirect |
| 164. #1332 | D79 | semidirect |
| 167. C79 | #11660 | semidirect |
| 234. Q16 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579184 | 2 |
| #23765197 | 2 |
| #23762157 | 2 |
| #23761364 | 2 |
| #23761362 | 2 |
| #23761360 | 2 |
| C79×#1332 | 2 |
| #11660 | 79 |