Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#19098996 | C2 | semidirect |
| 2. #23775159 | C2 | semidirect |
| 3. #23765650 | C2 | semidirect |
| 4. #23765487 | C2 | semidirect |
| 5. #23765440 | C2 | semidirect |
| 6. #23765326 | C2 | semidirect |
| 7. C16×D316 | C2 | semidirect |
| 8. C4×Q32×C79 | C2 | semidirect |
| 52. Q32×C79 | D4 | semidirect |
| 124. C4×C79 | #508 | semidirect |
| 140. C4×Q32 | D79 | semidirect |
| 142. C79 | #33853 | semidirect |
| 178. Q32 | D316 | semidirect |
| 259. C4 | #19098996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098996 | 2 |
| #23775159 | 2 |
| #23765650 | 2 |
| #23765487 | 2 |
| #23765440 | 2 |
| #23765326 | 2 |
| C16×D316 | 2 |
| C4×Q32×C79 | 2 |
| #33853 | 79 |