Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19149599 | C2 | semidirect |
| 3. C2×C4×#13063436 | C2 | semidirect |
| 4. #384×C173 | C2 | semidirect |
| 9. #19149676 | C4 | semidirect |
| 25. C2×#13063436 | D4 | semidirect |
| 63. C4×C173 | #102 | semidirect |
| 72. C173 | #1957 | semidirect |
| 77. #384 | D173 | semidirect |
| 136. C4 | #19149599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| C2×#19149599 | 2 |
| C2×C4×#13063436 | 2 |
| #384×C173 | 2 |
| #1957 | 173 |