Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
544 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#19149679 | C2 | semidirect |
| 3. #26011696 | C2 | direct (N × H) |
| 4. C2×C4⋊#13063436 | C2 | semidirect |
| 5. C2×#19149602 | C2 | semidirect |
| 12. #19149679 | C22 | semidirect |
| 15. C4⋊#13063436 | C22 | semidirect |
| 16. #19149602 | C22 | semidirect |
| 68. C2×C4×C173 | SD16 | semidirect |
| 86. C4×C173 | C2×SD16 | semidirect |
| 91. C2×C173 | #461 | semidirect |
| 95. C173 | C2×#461 | semidirect |
| 163. C2×C4 | #14583814 | semidirect |
| 183. C4 | C2×#14583814 | semidirect |
| 187. C2 | #26011696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| C2×#19149679 | 2 |
| #26011696 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149602 | 2 |
| C2×C4×D4×C173 | 2 |
| C2×#461 | 173 |