Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012496 | C2 | semidirect |
| 3. C4×C4⋊#10621924 | C2 | semidirect |
| 4. #26012361 | C2 | semidirect |
| 14. C4×Dic346 | C4 | semidirect |
| 15. #19149644 | C4 | semidirect |
| 16. D4×Dic173 | C4 | semidirect |
| 23. C4×D4×C173 | C4 | semidirect |
| 64. Dic346 | C4⋊C4 | semidirect |
| 83. D4×C173 | C4⋊C4 | semidirect |
| 106. Dic173 | #104 | semidirect |
| 115. C173 | #1806 | semidirect |
| 129. C4×D4 | #10621924 | semidirect |
| 181. D4 | C4⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012496 | 2 |
| C2×#19149743 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012361 | 2 |
| C4×#14583825 | 2 |
| #1806 | 173 |