Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 4. #26011583 | C2 | direct (N × H) |
| 10. C2×#14583816 | C4 | semidirect |
| 38. #14583816 | C2×C4 | semidirect |
| 68. C2×Dic173 | Q16 | semidirect |
| 97. Dic173 | C2×Q16 | semidirect |
| 98. C2×C173 | C4×Q16 | semidirect |
| 102. C173 | C2×C4×Q16 | semidirect |
| 201. C2 | #26011583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583816 | 2 |
| C2×Q8×Dic173 | 2 |
| C2×#19149644 | 2 |
| #26011583 | 2 |
| C2×#19149612 | 2 |
| C2×#19149604 | 2 |
| C2×C8×Dic173 | 2 |
| C2×#103×C173 | 2 |
| C2×C4×Q16 | 173 |