Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #26011865 | C2 | semidirect |
| 3. #26011841 | C2 | semidirect |
| 4. #26011693 | C2 | semidirect |
| 5. #26011630 | C2 | semidirect |
| 6. #26011544 | C2 | semidirect |
| 7. C2×C4⋊Q8×C173 | C2 | semidirect |
| 73. C2×C4×C173 | SD16 | semidirect |
| 100. C173 | #3206 | semidirect |
| 103. C2×C4⋊Q8 | D173 | semidirect |
| 173. C2×C4 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011865 | 2 |
| #26011841 | 2 |
| #26011693 | 2 |
| #26011630 | 2 |
| #26011544 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| #3206 | 173 |