Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19149710 | C2 | semidirect |
| 3. #26011713 | C2 | semidirect |
| 4. #26011701 | C2 | semidirect |
| 5. #26011691 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 7. #26011490 | C2 | semidirect |
| 8. C2×C4×Q8×C173 | C2 | semidirect |
| 52. C2×Q8×C173 | D4 | semidirect |
| 111. C4×C173 | #137 | semidirect |
| 120. C173 | #3037 | semidirect |
| 124. C2×C4×Q8 | D173 | semidirect |
| 160. C2×Q8 | D692 | semidirect |
| 233. C4 | #19149710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| #26012041 | 2 |
| #26011713 | 2 |
| #26011701 | 2 |
| #26011691 | 2 |
| #26011515 | 2 |
| #26011490 | 2 |
| C2×C4×Q8×C173 | 2 |
| #3037 | 173 |