Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #26012456 | C2 | semidirect |
| 3. C4×#14583836 | C2 | semidirect |
| 4. C4×D173⋊C8 | C2 | semidirect |
| 6. #19149767 | C4 | direct (N × H) |
| 20. #14583836 | C2×C4 | semidirect |
| 21. D173⋊C8 | C2×C4 | semidirect |
| 57. C4×C173 | #131 | semidirect |
| 59. Dic173 | #131 | semidirect |
| 65. C173 | C4×#131 | semidirect |
| 126. C4 | #19149767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| #26012456 | 2 |
| C4×#14583836 | 2 |
| C4×D173⋊C8 | 2 |
| C4×#14583827 | 2 |
| C4×#131 | 173 |