Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#19098702 | C2 | semidirect |
| 3. #23762368 | C2 | direct (N × H) |
| 4. C2×#19098296 | C2 | semidirect |
| 5. C2×#19098289 | C2 | semidirect |
| 6. C2×#395×C79 | C2 | semidirect |
| 17. #19098702 | C22 | semidirect |
| 20. #19098296 | C22 | semidirect |
| 21. #19098289 | C22 | semidirect |
| 26. #395×C79 | C22 | semidirect |
| 131. C22×C4×C79 | SD16 | semidirect |
| 177. C2×C4×C79 | C2×SD16 | semidirect |
| 219. C2×C79 | #1604 | semidirect |
| 226. C2×#395 | D79 | semidirect |
| 230. C79 | C2×#1604 | semidirect |
| 248. #395 | C2×D79 | semidirect |
| 346. C22×C4 | #11929611 | semidirect |
| 412. C2×C4 | C2×#11929611 | semidirect |
| 443. C2 | #23762368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099144 | 2 |
| C2×#19098702 | 2 |
| #23762368 | 2 |
| C2×#19098296 | 2 |
| C2×#19098289 | 2 |
| C2×#395×C79 | 2 |
| C2×#1604 | 79 |