Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#14583813 | C2 | semidirect |
| 3. C2×#19149603 | C2 | semidirect |
| 4. C2×#19149599 | C2 | semidirect |
| 5. C2×C22⋊#13063436 | C2 | semidirect |
| 6. #26011253 | C2 | semidirect |
| 7. C2×C22⋊Q8×C173 | C2 | semidirect |
| 46. C2×#13063436 | D4 | semidirect |
| 56. C2×Q8×C173 | D4 | semidirect |
| 69. C4⋊C4×C173 | D4 | semidirect |
| 94. C23×C173 | SD16 | semidirect |
| 157. C173 | #2000 | semidirect |
| 160. C2×C22⋊Q8 | D173 | semidirect |
| 194. C2×Q8 | C22⋊D173 | semidirect |
| 226. C4⋊C4 | C22⋊D173 | semidirect |
| 242. C23 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583813 | 2 |
| C2×#19149653 | 2 |
| C2×#19149603 | 2 |
| C2×#19149599 | 2 |
| C2×C22⋊#13063436 | 2 |
| #26011253 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #2000 | 173 |