Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| 13. C22×Dic346 | C4 | semidirect |
| 17. C2×Q8×D173 | C4 | semidirect |
| 21. C22×Q8×C173 | C4 | semidirect |
| 69. Dic346 | C22⋊C4 | semidirect |
| 84. Q8×C173 | C22⋊C4 | semidirect |
| 92. C22×C173 | #103 | semidirect |
| 98. C2×D173 | #103 | semidirect |
| 117. C173 | #1787 | semidirect |
| 130. C22×Q8 | #10621924 | semidirect |
| 187. Q8 | C22⋊#10621924 | semidirect |
| 219. C22 | #19149742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149742 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012433 | 2 |
| C22×Q8×D173 | 2 |
| #1787 | 173 |