Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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. #26012501 | C2 | semidirect |
| 3. #26012359 | C2 | semidirect |
| 13. C2×#14583809 | C4 | semidirect |
| 15. C22×#13063436 | C4 | semidirect |
| 16. C2×C8×D173 | C4 | semidirect |
| 18. C2×M16×C173 | C4 | semidirect |
| 85. C173 | #1812 | semidirect |
| 96. C2×M16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012501 | 2 |
| #26012470 | 2 |
| #26012359 | 2 |
| C2×#19149687 | 2 |
| #1812 | 173 |