Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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. #26012507 | C2 | semidirect |
| 2. C2×C4⋊#13063443 | C2 | semidirect |
| 3. Q8⋊#13063443 | C2 | semidirect |
| 4. D4⋊#13063443 | C2 | semidirect |
| 45. #41×C173 | C8 | semidirect |
| 68. Q8×C173 | C2×C8 | semidirect |
| 71. D4×C173 | C2×C8 | semidirect |
| 101. C173 | #1477 | semidirect |
| 126. #41 | #13063443 | semidirect |
| 156. Q8 | C2×#13063443 | semidirect |
| 159. D4 | C2×#13063443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012507 | 2 |
| C2×C4⋊#13063443 | 2 |
| Q8⋊#13063443 | 2 |
| D4⋊#13063443 | 2 |
| #41×Dic173 | 2 |
| #1477 | 173 |