Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19149702 | C2 | semidirect |
| 2. C2×Q16×D173 | C2 | semidirect |
| 3. #26012153 | C2 | semidirect |
| 4. #26011875 | C2 | semidirect |
| 5. #26011733 | C2 | semidirect |
| 6. #26011728 | C2 | semidirect |
| 7. #26011713 | C2 | semidirect |
| 8. #26011656 | C2 | semidirect |
| 9. #26011631 | C2 | semidirect |
| 10. C8×D692 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 73. Q16×C173 | D4 | semidirect |
| 120. C2×D173 | #135 | semidirect |
| 136. C173 | #3285 | semidirect |
| 147. C4×Q16 | D173 | semidirect |
| 195. Q16 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C2×Q16×D173 | 2 |
| #26012153 | 2 |
| #26011875 | 2 |
| #26011733 | 2 |
| #26011728 | 2 |
| #26011713 | 2 |
| #26011656 | 2 |
| #26011631 | 2 |
| C8×D692 | 2 |
| C4×Q16×C173 | 2 |
| #3285 | 173 |