Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
650 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23765761 | C2 | semidirect |
| 2. #23764320 | C2 | semidirect |
| 3. #23761908 | C2 | semidirect |
| 4. #23761843 | C2 | semidirect |
| 5. #23761292 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 24. #476×C79 | C4 | semidirect |
| 25. #459×C79 | C4 | semidirect |
| 52. C4⋊Q8×C79 | C2×C4 | semidirect |
| 53. #127×C79 | C2×C4 | semidirect |
| 67. C4⋊C8×C79 | C2×C4 | semidirect |
| 135. D4×C79 | #104 | semidirect |
| 204. C79 | #9325 | semidirect |
| 209. #476 | Dic79 | semidirect |
| 210. #459 | Dic79 | semidirect |
| 232. C4⋊Q8 | C2×Dic79 | semidirect |
| 233. #127 | C2×Dic79 | semidirect |
| 254. C4⋊C8 | C2×Dic79 | semidirect |
| 332. D4 | #14579088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765761 | 2 |
| #23764320 | 2 |
| #23761908 | 2 |
| #23761843 | 2 |
| #23761292 | 2 |
| #23761257 | 2 |
| C79×#3109 | 2 |
| #9325 | 79 |