Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23773205 | C2 | semidirect |
| 5. #23761900 | C2 | semidirect |
| 6. #23761302 | C2 | semidirect |
| 7. C79×#1479 | C2 | semidirect |
| 115. C2×Q8×C79 | SD16 | semidirect |
| 213. #1479 | D79 | semidirect |
| 215. C79 | #10250 | semidirect |
| 293. C2×Q8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774343 | 2 |
| #23773205 | 2 |
| #23768399 | 2 |
| #23762067 | 2 |
| #23761900 | 2 |
| #23761302 | 2 |
| C79×#1479 | 2 |
| #10250 | 79 |