Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 3. #26012362 | C2 | semidirect |
| 4. #26012358 | C2 | semidirect |
| 17. #19149638 | C4 | semidirect |
| 18. #19149636 | C4 | semidirect |
| 20. C42×D173 | C4 | semidirect |
| 22. C2×C42×C173 | C4 | semidirect |
| 102. C173 | #1827 | semidirect |
| 121. C2×C42 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012477 | 2 |
| #26012470 | 2 |
| #26012362 | 2 |
| #26012358 | 2 |
| C4×#14583826 | 2 |
| #1827 | 173 |