Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765552 | C2 | semidirect |
| 4. #23761464 | C2 | semidirect |
| 5. #23761459 | C2 | semidirect |
| 7. C8×Q16×C79 | C2 | semidirect |
| 59. Q16×C79 | SD16 | semidirect |
| 112. C8×Q16 | D79 | semidirect |
| 116. C79 | #12419 | semidirect |
| 160. Q16 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765552 | 2 |
| #23765440 | 2 |
| #23762992 | 2 |
| #23761464 | 2 |
| #23761459 | 2 |
| #23761445 | 2 |
| C8×Q16×C79 | 2 |
| #12419 | 79 |