Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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×#19149620 | C2 | semidirect |
| 2. #26011868 | C2 | semidirect |
| 3. C4×#14583801 | C2 | semidirect |
| 4. #493×C173 | C2 | semidirect |
| 18. #14583801 | D4 | semidirect |
| 43. C4×C173 | D16 | semidirect |
| 50. C173 | #2246 | semidirect |
| 54. #493 | D173 | semidirect |
| 94. C4 | #19149620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149620 | 2 |
| #26011868 | 2 |
| C4×#14583801 | 2 |
| #493×C173 | 2 |
| #2246 | 173 |