Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23776550 | C2 | semidirect |
| 2. #23765712 | C2 | semidirect |
| 3. C2×#19098402 | C2 | semidirect |
| 4. #23765521 | C2 | semidirect |
| 5. #23761592 | C2 | semidirect |
| 6. #23761541 | C2 | semidirect |
| 7. C79×#1417 | C2 | semidirect |
| 124. #1417 | D79 | semidirect |
| 126. C79 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776550 | 2 |
| #23765712 | 2 |
| C2×#19098402 | 2 |
| #23765521 | 2 |
| #23761592 | 2 |
| #23761541 | 2 |
| C79×#1417 | 2 |
| #13670 | 79 |