Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26011542 | C2 | semidirect |
| 3. C4⋊C8×D173 | C2 | semidirect |
| 4. Q8⋊#13063436 | C2 | semidirect |
| 5. #26011220 | C2 | semidirect |
| 6. #26011218 | C2 | semidirect |
| 7. Q8⋊C8×C173 | C2 | semidirect |
| 28. #14583827 | C8 | semidirect |
| 61. D692 | C2×C8 | semidirect |
| 78. Q8×C173 | C2×C8 | semidirect |
| 109. C173 | #1477 | semidirect |
| 115. Q8⋊C8 | D173 | semidirect |
| 170. Q8 | C8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583827 | 2 |
| #26011542 | 2 |
| C4⋊C8×D173 | 2 |
| Q8⋊#13063436 | 2 |
| #26011220 | 2 |
| #26011218 | 2 |
| Q8⋊C8×C173 | 2 |
| #1477 | 173 |