Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23765440 | C2 | semidirect |
| 3. Q16×C79⋊C8 | C2 | semidirect |
| 4. #23761469 | C2 | semidirect |
| 5. #23761447 | C2 | semidirect |
| 6. #23761446 | C2 | semidirect |
| 7. C79×#2207 | C2 | semidirect |
| 65. Q16×C79 | D8 | semidirect |
| 101. C79⋊C8 | SD32 | semidirect |
| 123. #2207 | D79 | semidirect |
| 129. C79 | #12425 | semidirect |
| 176. Q16 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765440 | 2 |
| #23763014 | 2 |
| Q16×C79⋊C8 | 2 |
| #23761469 | 2 |
| #23761447 | 2 |
| #23761446 | 2 |
| C79×#2207 | 2 |
| #12425 | 79 |