Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
276 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26012510 | C2 | semidirect |
| 2. C4×D173⋊C8 | C2 | semidirect |
| 3. Q8⋊#13063443 | C2 | semidirect |
| 4. #26012339 | C2 | semidirect |
| 27. #14583827 | C8 | semidirect |
| 57. D692 | C2×C8 | semidirect |
| 70. Q8×C173 | C2×C8 | semidirect |
| 98. C173 | #1476 | semidirect |
| 153. Q8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012510 | 2 |
| C4×D173⋊C8 | 2 |
| Q8⋊#13063443 | 2 |
| #26012339 | 2 |
| C4×#14583827 | 2 |
| #1476 | 173 |