Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D173 | C2 | semidirect |
| 3. #26011803 | C2 | semidirect |
| 4. #26011787 | C2 | semidirect |
| 5. #26011786 | C2 | semidirect |
| 6. #26011688 | C2 | semidirect |
| 7. #26011628 | C2 | semidirect |
| 8. #26011592 | C2 | semidirect |
| 9. #26011588 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 87. Dic346 | #41 | semidirect |
| 105. Q8×C173 | #41 | semidirect |
| 140. C173 | #3112 | semidirect |
| 148. #460 | D173 | semidirect |
| 231. Q8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| C4×Q8×D173 | 2 |
| #26011803 | 2 |
| #26011787 | 2 |
| #26011786 | 2 |
| #26011688 | 2 |
| #26011628 | 2 |
| #26011592 | 2 |
| #26011588 | 2 |
| #26011547 | 2 |
| #460×C173 | 2 |
| #3112 | 173 |