Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 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 |
|---|---|---|
| 9. #19149586 | C4 | semidirect |
| 10. C22×Q8×C173 | C4 | semidirect |
| 71. C173 | #1351 | semidirect |
| 76. C22×Q8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012369 | 2 |
| #26012335 | 2 |
| #26011402 | 2 |
| #1351 | 173 |