Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 108. C42×C79 | Q16 | semidirect |
| 180. C79 | #10523 | semidirect |
| 281. C42 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774742 | 2 |
| #23764377 | 2 |
| #23763517 | 2 |
| #23762091 | 2 |
| #23762090 | 2 |
| #23761274 | 2 |
| C79×#1994 | 2 |
| #10523 | 79 |