Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 41. C4⋊Q8×C79 | Q8 | semidirect |
| 42. C4⋊Q8×C79 | Q8 | semidirect |
| 161. C79 | #10363 | semidirect |
| 181. C4⋊Q8 | Dic158 | semidirect |
| 182. C4⋊Q8 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771776 | 2 |
| #23764378 | 2 |
| #23761964 | 2 |
| #23761259 | 2 |
| #23761258 | 2 |
| #23761232 | 2 |
| C79×#1518 | 2 |
| #10363 | 79 |