Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #23765667 | C2 | semidirect |
| 2. #23765435 | C2 | semidirect |
| 3. #23762884 | C2 | semidirect |
| 4. #23761443 | C2 | semidirect |
| 5. #23761382 | C2 | semidirect |
| 6. #23761367 | C2 | semidirect |
| 7. C79×#3403 | C2 | semidirect |
| 162. #3403 | D79 | semidirect |
| 169. C79 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765667 | 2 |
| #23765435 | 2 |
| #23762884 | 2 |
| #23761443 | 2 |
| #23761382 | 2 |
| #23761367 | 2 |
| C79×#3403 | 2 |
| #12336 | 79 |