Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
164 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×#19149754 | C2 | semidirect |
| 2. C2×D173⋊C16 | C2 | semidirect |
| 3. C4⋊#14583829 | C2 | semidirect |
| 4. #26012386 | C2 | semidirect |
| 5. #26012386 | C2 | semidirect |
| 6. #26012379 | C2 | semidirect |
| 24. #14583829 | D4 | semidirect |
| 63. C2×D173 | M32 | semidirect |
| 75. C173 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149754 | 2 |
| C2×D173⋊C16 | 2 |
| C4⋊#14583829 | 2 |
| #26012386 | 2 |
| #26012379 | 2 |
| #26011556 | 2 |
| #2168 | 173 |