Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 32 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. #26012386 | C2 | semidirect |
| 2. #26012365 | C2 | semidirect |
| 6. C2×D1384 | C4 | semidirect |
| 10. #107×C173 | C4 | semidirect |
| 59. C173 | #1347 | semidirect |
| 69. #107 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012386 | 2 |
| #26012365 | 2 |
| #26011728 | 2 |
| #1347 | 173 |