Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19098371 | C2 | semidirect |
| 3. #23765110 | C2 | semidirect |
| 4. C2×#19098346 | C2 | semidirect |
| 5. #23763465 | C2 | semidirect |
| 6. #23761508 | C2 | semidirect |
| 7. C2×#366×C79 | C2 | semidirect |
| 63. C2×C16×C79 | D4 | semidirect |
| 185. C2×#366 | D79 | semidirect |
| 191. C79 | #13384 | semidirect |
| 241. C2×C16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773072 | 2 |
| C2×#19098371 | 2 |
| #23765110 | 2 |
| C2×#19098346 | 2 |
| #23763465 | 2 |
| #23761508 | 2 |
| C2×#366×C79 | 2 |
| #13384 | 79 |