Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012509 | C2 | semidirect |
| 2. D173⋊(C4⋊C8) | C2 | semidirect |
| 3. Q8⋊#13063443 | C2 | semidirect |
| 4. #26012339 | C2 | semidirect |
| 27. #14583827 | C8 | semidirect |
| 57. D692 | C2×C8 | semidirect |
| 72. Q8×C173 | C2×C8 | semidirect |
| 101. C173 | #1477 | semidirect |
| 156. Q8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012509 | 2 |
| D173⋊(C4⋊C8) | 2 |
| Q8⋊#13063443 | 2 |
| #26012339 | 2 |
| C4×#14583827 | 2 |
| #1477 | 173 |