Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19149712 | C2 | semidirect |
| 3. C2×#19149679 | C2 | semidirect |
| 4. #26011885 | C2 | semidirect |
| 5. #26011871 | C2 | semidirect |
| 6. #26011864 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 44. M16×C173 | D4 | semidirect |
| 75. C4×C173 | #137 | semidirect |
| 83. C173 | #3152 | semidirect |
| 91. C4×M16 | D173 | semidirect |
| 124. M16 | D692 | semidirect |
| 161. C4 | #19149712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| #26012041 | 2 |
| C2×#19149679 | 2 |
| #26011885 | 2 |
| #26011871 | 2 |
| #26011864 | 2 |
| C4×M16×C173 | 2 |
| #3152 | 173 |