Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011865 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011691 | C2 | semidirect |
| 5. #26011641 | C2 | semidirect |
| 6. #26011544 | C2 | semidirect |
| 7. #533×C173 | C2 | semidirect |
| 11. C2×#14583813 | C22 | semidirect |
| 16. C4⋊#13063436 | C22 | semidirect |
| 17. #19149599 | C22 | semidirect |
| 19. C4×#13063436 | C22 | semidirect |
| 20. C4⋊Q8×C173 | C22 | semidirect |
| 21. C4⋊Q8×C173 | C22 | semidirect |
| 26. C4×Q8×C173 | C22 | semidirect |
| 76. C2×C4×C173 | SD16 | semidirect |
| 104. C173 | #3208 | semidirect |
| 106. #533 | D173 | semidirect |
| 117. C4⋊Q8 | C2×D173 | semidirect |
| 118. C4⋊Q8 | C2×D173 | semidirect |
| 127. C4×Q8 | C2×D173 | semidirect |
| 180. C2×C4 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| #26011865 | 2 |
| #26011839 | 2 |
| #26011691 | 2 |
| #26011641 | 2 |
| #26011544 | 2 |
| #533×C173 | 2 |
| #3208 | 173 |