Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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. #26012559 | C2 | semidirect |
| 2. #26012471 | C2 | semidirect |
| 3. #26012470 | C2 | semidirect |
| 11. C2×#14583825 | C4 | semidirect |
| 13. C22×Dic346 | C4 | semidirect |
| 14. C2×Q8×D173 | C4 | semidirect |
| 16. C2×#41×C173 | C4 | semidirect |
| 76. C173 | #2884 | semidirect |
| 86. C2×#41 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012559 | 2 |
| #26012471 | 2 |
| #26012470 | 2 |
| C2×#19149726 | 2 |
| #2884 | 173 |