Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 147 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. #23763321 | C2 | semidirect |
| 2. #23761904 | C2 | semidirect |
| 3. #23761641 | C2 | semidirect |
| 7. #19098527 | C22 | semidirect |
| 8. C2×C79⋊#95 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C79 | C4 | semidirect |
| 15. #535×C79 | C4 | semidirect |
| 19. #518×C79 | C4 | semidirect |
| 76. C2×Q8×C79 | C22⋊C4 | semidirect |
| 94. C2×D4×C79 | C22⋊C4 | semidirect |
| 103. C4⋊C4×C79 | C22⋊C4 | semidirect |
| 203. C79 | #8453 | semidirect |
| 204. C2×H(5,𝔽2) | Dic79 | semidirect |
| 208. #535 | Dic79 | semidirect |
| 212. #518 | Dic79 | semidirect |
| 267. C2×Q8 | C22⋊Dic79 | semidirect |
| 285. C2×D4 | C22⋊Dic79 | semidirect |
| 301. C4⋊C4 | C22⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763321 | 2 |
| #23761904 | 2 |
| #23761641 | 2 |
| C79×#3484 | 2 |
| #8453 | 79 |