Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #23765119 | C2 | semidirect |
| 4. C2×#19098368 | C2 | semidirect |
| 6. #23761510 | C2 | semidirect |
| 7. C79×#1382 | C2 | semidirect |
| 14. #19098839 | C4 | semidirect |
| 38. C2×Dic316 | C2×C4 | semidirect |
| 68. #108×C79 | C2×C4 | semidirect |
| 188. #1382 | D79 | semidirect |
| 189. C79 | #12997 | semidirect |
| 245. #108 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098839 | 2 |
| #23771997 | 2 |
| #23765119 | 2 |
| C2×#19098368 | 2 |
| C2×#19098346 | 2 |
| #23761510 | 2 |
| C79×#1382 | 2 |
| #12997 | 79 |