Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766510 | C2 | semidirect |
| 3. #23762023 | C2 | semidirect |
| 4. #23761908 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 7. C79×#1505 | C2 | semidirect |
| 11. #19098955 | C4 | semidirect |
| 12. #19098950 | C4 | semidirect |
| 58. #14579072 | C2×C4 | semidirect |
| 66. C4⋊Q8×C79 | C2×C4 | semidirect |
| 67. #127×C79 | C2×C4 | semidirect |
| 231. #1505 | D79 | semidirect |
| 234. C79 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D79 | semidirect |
| 272. #127 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773868 | 2 |
| #23766510 | 2 |
| #23762023 | 2 |
| #23761908 | 2 |
| #23761293 | 2 |
| #23761292 | 2 |
| C79×#1505 | 2 |
| #9441 | 79 |