Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1174 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23774327 | C2 | semidirect |
| 3. #23768605 | C2 | semidirect |
| 4. #23762371 | C2 | semidirect |
| 5. #23761896 | C2 | semidirect |
| 6. C79×#1461 | C2 | semidirect |
| 109. C2×Q8×C79 | SD16 | semidirect |
| 186. #1461 | D79 | semidirect |
| 187. C79 | #18402 | semidirect |
| 267. C2×Q8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777171 | 2 |
| #23774327 | 2 |
| #23768605 | 2 |
| #23762371 | 2 |
| #23761896 | 2 |
| C79×#1461 | 2 |
| #18402 | 79 |