Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 15. #19149590 | C4 | semidirect |
| 16. #19149589 | C4 | semidirect |
| 17. C8×Dic173 | C4 | semidirect |
| 18. C4×C8×C173 | C4 | semidirect |
| 72. C173 | #1833 | semidirect |
| 91. C4×C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#108 | 2 |
| #26012501 | 2 |
| #26012373 | 2 |
| #26012358 | 2 |
| #26011445 | 2 |
| #1833 | 173 |