Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
270 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. #26012472 | C2 | semidirect |
| 2. #26012396 | C2 | semidirect |
| 3. #26012395 | C2 | semidirect |
| 7. #19149738 | C22 | semidirect |
| 9. C2×D4×D173 | C4 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 15. #19149636 | C4 | semidirect |
| 16. #124×C173 | C4 | semidirect |
| 84. C173 | #2128 | semidirect |
| 95. #124 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012472 | 2 |
| #26012396 | 2 |
| #26012395 | 2 |
| #26012059 | 2 |
| #2128 | 173 |