Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
618 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 88 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×#19149744 | C2 | semidirect |
| 2. C2×#19149743 | C2 | semidirect |
| 3. #26012462 | C2 | semidirect |
| 4. C4×C22⋊#10621924 | C2 | semidirect |
| 6. C2×#14583836 | C22 | semidirect |
| 8. C2×C4×#10621924 | C22 | semidirect |
| 16. C2×#14583826 | C4 | semidirect |
| 21. C2×Q8×D173 | C4 | semidirect |
| 23. C2×D4×D173 | C4 | semidirect |
| 26. C2×#41×C173 | C4 | semidirect |
| 90. Dic346 | C22⋊C4 | semidirect |
| 93. D692 | C22⋊C4 | semidirect |
| 114. Q8×C173 | C22⋊C4 | semidirect |
| 117. D4×C173 | C22⋊C4 | semidirect |
| 140. C2×D173 | #104 | semidirect |
| 158. C173 | #1789 | semidirect |
| 172. C2×#41 | #10621924 | semidirect |
| 249. Q8 | C22⋊#10621924 | semidirect |
| 258. D4 | C22⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149744 | 2 |
| C2×#19149743 | 2 |
| #26012462 | 2 |
| C4×C22⋊#10621924 | 2 |
| C2×#41×D173 | 2 |
| #1789 | 173 |