Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26011513 | C2 | semidirect |
| 3. C4×#14583809 | C2 | semidirect |
| 4. Q8⋊#13063436 | C2 | semidirect |
| 5. #26011220 | C2 | semidirect |
| 6. #26011218 | C2 | semidirect |
| 7. Q8⋊C8×C173 | C2 | semidirect |
| 62. D692 | M16 | semidirect |
| 79. Q8×C173 | M16 | semidirect |
| 110. C173 | #1489 | semidirect |
| 116. Q8⋊C8 | D173 | semidirect |
| 172. Q8 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583827 | 2 |
| #26011513 | 2 |
| C4×#14583809 | 2 |
| Q8⋊#13063436 | 2 |
| #26011220 | 2 |
| #26011218 | 2 |
| Q8⋊C8×C173 | 2 |
| #1489 | 173 |