Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 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. C2×#19149742 | C2 | semidirect |
| 2. C2×#19149741 | C2 | semidirect |
| 3. D173⋊(C22⋊C8) | C2 | semidirect |
| 4. #26012433 | C2 | semidirect |
| 14. C2×#14583827 | C4 | semidirect |
| 16. C2×#14583826 | C4 | semidirect |
| 18. C2×#14583825 | C4 | semidirect |
| 26. C2×#41×C173 | C4 | semidirect |
| 92. Dic346 | C22⋊C4 | semidirect |
| 95. D692 | C22⋊C4 | semidirect |
| 116. Q8×C173 | C22⋊C4 | semidirect |
| 119. D4×C173 | C22⋊C4 | semidirect |
| 164. C173 | #1788 | semidirect |
| 178. C2×#41 | #10621924 | semidirect |
| 257. Q8 | C22⋊#10621924 | semidirect |
| 266. D4 | C22⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149742 | 2 |
| C2×#19149741 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012433 | 2 |
| C2×#41×D173 | 2 |
| #1788 | 173 |