Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19149700 | C2 | semidirect |
| 2. #26012163 | C2 | semidirect |
| 3. #26012145 | C2 | semidirect |
| 4. #26011864 | C2 | semidirect |
| 5. #26011721 | C2 | semidirect |
| 6. #26011701 | C2 | semidirect |
| 7. #26011686 | C2 | semidirect |
| 8. #26011656 | C2 | semidirect |
| 9. #26011637 | C2 | semidirect |
| 10. C8×D692 | C2 | semidirect |
| 11. C4×SD16×C173 | C2 | semidirect |
| 73. SD16×C173 | D4 | semidirect |
| 129. C4×C173 | #135 | semidirect |
| 140. C173 | #3284 | semidirect |
| 151. C4×SD16 | D173 | semidirect |
| 204. SD16 | D692 | semidirect |
| 272. C4 | #19149700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149700 | 2 |
| #26012163 | 2 |
| #26012145 | 2 |
| #26011864 | 2 |
| #26011721 | 2 |
| #26011701 | 2 |
| #26011686 | 2 |
| #26011656 | 2 |
| #26011637 | 2 |
| C8×D692 | 2 |
| C4×SD16×C173 | 2 |
| #3284 | 173 |