Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #23764374 | C2 | semidirect |
| 5. #23761282 | C2 | semidirect |
| 6. #23761281 | C2 | semidirect |
| 7. C79×#1993 | C2 | semidirect |
| 12. #19098955 | C4 | semidirect |
| 57. #14579072 | C2×C4 | semidirect |
| 67. C4⋊Q8×C79 | C2×C4 | semidirect |
| 224. #1993 | D79 | semidirect |
| 228. C79 | #9003 | semidirect |
| 267. C4⋊Q8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098955 | 2 |
| #23766571 | 2 |
| #23764374 | 2 |
| C2×#19098302 | 2 |
| #23761282 | 2 |
| #23761281 | 2 |
| C79×#1993 | 2 |
| #9003 | 79 |