Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012227 | C2 | semidirect |
| 2. #26012202 | C2 | semidirect |
| 3. #26011844 | C2 | semidirect |
| 4. #26011793 | C2 | semidirect |
| 5. #26011783 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 8. C8×Dic346 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. #26011571 | C2 | semidirect |
| 11. #486×C173 | C2 | semidirect |
| 122. C173 | #3361 | semidirect |
| 127. #486 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012227 | 2 |
| #26012202 | 2 |
| #26011844 | 2 |
| #26011793 | 2 |
| #26011783 | 2 |
| #26011705 | 2 |
| #26011683 | 2 |
| C8×Dic346 | 2 |
| C4×#14583815 | 2 |
| #26011571 | 2 |
| #486×C173 | 2 |
| #3361 | 173 |