Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26011969 | C2 | semidirect |
| 3. #26011500 | C2 | semidirect |
| 5. #26011262 | C2 | semidirect |
| 6. #26011248 | C2 | semidirect |
| 22. C2×Q16×C173 | C4 | semidirect |
| 23. C2×SD16×C173 | C4 | semidirect |
| 109. C173 | #1905 | semidirect |
| 122. C2×Q16 | Dic173 | semidirect |
| 123. C2×SD16 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011969 | 2 |
| #26011508 | 2 |
| #26011500 | 2 |
| #26011465 | 2 |
| #26011262 | 2 |
| #26011248 | 2 |
| C2×#137×C173 | 2 |
| #1905 | 173 |