Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1112 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 581 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. #26012221 | C2 | direct (N × H) |
| 23. C2×Dic346 | Q8 | semidirect |
| 41. Dic346 | C2×Q8 | semidirect |
| 62. C2×C173 | Q82 | semidirect |
| 65. C173 | C2×Q82 | semidirect |
| 128. C2 | #26012221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012221 | 2 |
| C2×#19149678 | 2 |
| C2×#19149677 | 2 |
| C2×C4×Dic346 | 2 |
| C2×#19149644 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| C2×Q82 | 173 |