Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. #23776375 | C2 | semidirect |
| 2. Q8×D632 | C2 | semidirect |
| 3. #23765624 | C2 | semidirect |
| 4. #23765538 | C2 | semidirect |
| 5. #23765436 | C2 | semidirect |
| 6. C4×D1264 | C2 | semidirect |
| 7. Q8×C16×C79 | C2 | semidirect |
| 59. D632 | #41 | semidirect |
| 74. Q8×C79 | D16 | semidirect |
| 116. Q8×C16 | D79 | semidirect |
| 118. C79 | #33925 | semidirect |
| 186. Q8 | D1264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776375 | 2 |
| Q8×D632 | 2 |
| #23765624 | 2 |
| #23765538 | 2 |
| #23765436 | 2 |
| C4×D1264 | 2 |
| Q8×C16×C79 | 2 |
| #33925 | 79 |