Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 4. #23761561 | C2 | semidirect |
| 5. #23761560 | C2 | semidirect |
| 6. #23761559 | C2 | semidirect |
| 7. C79×#1407 | C2 | semidirect |
| 10. C4⋊Q8×D79 | C4 | semidirect |
| 13. #19098957 | C4 | semidirect |
| 15. #19098955 | C4 | semidirect |
| 19. #97×D79 | C4 | semidirect |
| 42. #14579161 | C2×C4 | semidirect |
| 57. #14579072 | C2×C4 | semidirect |
| 61. C4⋊Q8×C79 | C2×C4 | semidirect |
| 65. #97×C79 | C2×C4 | semidirect |
| 184. D79 | #1407 | direct (N × H) |
| 191. #1407 | D79 | direct (N × H) |
| 192. C79 | C2×#1407 | semidirect |
| 232. C4⋊Q8 | C4×D79 | semidirect |
| 250. #97 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #497×D79 | 2 |
| #355×D79 | 2 |
| #354×D79 | 2 |
| #23761561 | 2 |
| #23761560 | 2 |
| #23761559 | 2 |
| C79×#1407 | 2 |
| C2×#1407 | 79 |