Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 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. #23772316 | C2 | semidirect |
| 3. C2×#19098375 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. #23764308 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 7. C79×#1385 | C2 | semidirect |
| 13. C2×#14579106 | C4 | semidirect |
| 14. C2×D1264 | C4 | semidirect |
| 176. #1385 | D79 | semidirect |
| 178. C79 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| #23772316 | 2 |
| C2×#19098375 | 2 |
| #23765127 | 2 |
| #23764308 | 2 |
| #23761485 | 2 |
| C79×#1385 | 2 |
| #13036 | 79 |