Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23761430 | C2 | semidirect |
| 4. #23761344 | C2 | semidirect |
| 5. C79×#2844 | C2 | semidirect |
| 75. C42×C79 | SD16 | semidirect |
| 132. #2844 | D79 | semidirect |
| 137. C79 | #12184 | semidirect |
| 207. C42 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764629 | 2 |
| #23762368 | 2 |
| #23761430 | 2 |
| #23761344 | 2 |
| C79×#2844 | 2 |
| #12184 | 79 |