Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19149594 | C2 | semidirect |
| 2. #26011354 | C2 | semidirect |
| 9. C22×Q8×C173 | C4 | semidirect |
| 10. C22×D4×C173 | C4 | semidirect |
| 12. C23×C4×C173 | C4 | semidirect |
| 75. C173 | #1782 | semidirect |
| 82. C22×Q8 | Dic173 | semidirect |
| 83. C22×D4 | Dic173 | semidirect |
| 85. C23×C4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149594 | 2 |
| #26011354 | 2 |
| C22×#41×C173 | 2 |
| #1782 | 173 |