Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 11. #19149644 | C4 | semidirect |
| 17. #19149604 | C4 | semidirect |
| 18. #19149602 | C4 | semidirect |
| 57. Dic346 | C42 | semidirect |
| 101. Dic173 | #103 | semidirect |
| 109. C173 | C4×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149644 | 2 |
| C2×#19149604 | 2 |
| C2×#19149602 | 2 |
| C2×C8×Dic173 | 2 |
| C4⋊C4×Dic173 | 2 |
| #26011253 | 2 |
| #340×C173 | 2 |
| C4×#103 | 173 |