Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #23765194 | C2 | semidirect |
| 5. #23761513 | C2 | semidirect |
| 6. #23761482 | C2 | semidirect |
| 7. C4×#108×C79 | C2 | semidirect |
| 15. #19098378 | C4 | semidirect |
| 16. #19098375 | C4 | semidirect |
| 146. C4×#108 | D79 | semidirect |
| 149. C79 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765194 | 2 |
| #23765147 | 2 |
| #23765127 | 2 |
| #23764288 | 2 |
| #23761513 | 2 |
| #23761482 | 2 |
| C4×#108×C79 | 2 |
| #13137 | 79 |