Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 8. C2×#14583829 | C4 | semidirect |
| 12. #19149619 | C4 | semidirect |
| 15. M32×C173 | C4 | semidirect |
| 58. C173 | #1378 | semidirect |
| 70. M32 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149754 | 2 |
| #26012454 | 2 |
| M32×D173 | 2 |
| #1378 | 173 |