Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
274 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23761470 | C2 | semidirect |
| 4. #23761445 | C2 | semidirect |
| 5. C8×Q16×C79 | C2 | semidirect |
| 47. Q16×C79 | D8 | semidirect |
| 75. C8×C79 | SD32 | semidirect |
| 96. C8×Q16 | D79 | semidirect |
| 99. C79 | #12425 | semidirect |
| 134. Q16 | D632 | semidirect |
| 169. C8 | #14579104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765440 | 2 |
| #23763015 | 2 |
| #23761470 | 2 |
| #23761445 | 2 |
| C8×Q16×C79 | 2 |
| #12425 | 79 |