Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23768305 | C2 | semidirect |
| 3. #23761960 | C2 | semidirect |
| 4. #23761824 | C2 | semidirect |
| 5. #23761795 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#3037 | C2 | semidirect |
| 120. C2×Q8×C79 | D8 | semidirect |
| 245. #3037 | D79 | semidirect |
| 251. C79 | #9997 | semidirect |
| 341. C2×Q8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773396 | 2 |
| #23768305 | 2 |
| #23761960 | 2 |
| #23761824 | 2 |
| #23761795 | 2 |
| #23761260 | 2 |
| C79×#3037 | 2 |
| #9997 | 79 |