Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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. D173⋊(C4⋊C8) | C2 | semidirect |
| 3. #26012437 | C2 | semidirect |
| 4. #26012364 | C2 | semidirect |
| 15. C4×D692 | C4 | semidirect |
| 16. D4×Dic173 | C4 | semidirect |
| 17. #19149641 | C4 | semidirect |
| 23. C4×D4×C173 | C4 | semidirect |
| 74. D692 | C4⋊C4 | semidirect |
| 96. D4×C173 | C4⋊C4 | semidirect |
| 122. C4×C173 | #102 | semidirect |
| 127. Dic173 | #102 | semidirect |
| 139. C173 | #1802 | semidirect |
| 154. C4×D4 | #10621924 | semidirect |
| 215. D4 | C4⋊#10621924 | semidirect |
| 267. C4 | #19149741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C4⋊C8) | 2 |
| C2×#19149741 | 2 |
| #26012437 | 2 |
| #26012364 | 2 |
| C4×D4×D173 | 2 |
| #1802 | 173 |