Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19099004 | C2 | semidirect |
| 3. C2×#19098374 | C2 | semidirect |
| 4. C2×#19098373 | C2 | semidirect |
| 5. #23764272 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 7. C2×#510×C79 | C2 | semidirect |
| 59. #14579101 | D4 | semidirect |
| 79. C2×Q16×C79 | D4 | semidirect |
| 86. M32×C79 | D4 | semidirect |
| 222. C2×#510 | D79 | semidirect |
| 228. C79 | #13342 | semidirect |
| 275. C2×Q16 | C22⋊D79 | semidirect |
| 300. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773843 | 2 |
| C2×#19098374 | 2 |
| C2×#19098373 | 2 |
| #23764272 | 2 |
| #23761483 | 2 |
| C2×#510×C79 | 2 |
| #13342 | 79 |