Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011974 | C2 | semidirect |
| 3. #26011497 | C2 | semidirect |
| 4. #26011393 | C2 | semidirect |
| 5. #26011259 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C2×#104×C173 | C2 | semidirect |
| 10. #19149704 | C4 | semidirect |
| 34. C2×D692 | C2×C4 | semidirect |
| 40. #14583810 | C2×C4 | semidirect |
| 85. Q8×C173 | C22⋊C4 | semidirect |
| 89. D4×C173 | C22⋊C4 | semidirect |
| 132. C173 | #1883 | semidirect |
| 136. C2×#104 | D173 | semidirect |
| 208. Q8 | #14583803 | semidirect |
| 216. D4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| #26011974 | 2 |
| #26011497 | 2 |
| #26011393 | 2 |
| #26011259 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1883 | 173 |