Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. #26012369 | C2 | semidirect |
| 8. C23×Dic173 | C4 | semidirect |
| 11. C2×#14583803 | C4 | semidirect |
| 13. C23×C4×C173 | C4 | semidirect |
| 100. C173 | #1819 | semidirect |
| 107. C23×C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012432 | 2 |
| #26012369 | 2 |
| C22×#14583803 | 2 |
| #1819 | 173 |