Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14583816 | C2 | semidirect |
| 3. #26011870 | C2 | semidirect |
| 4. #26011730 | C2 | semidirect |
| 5. #26011701 | C2 | semidirect |
| 6. #26011698 | C2 | semidirect |
| 7. #26011647 | C2 | semidirect |
| 8. #26011646 | C2 | semidirect |
| 9. C4×#14583816 | C2 | semidirect |
| 52. #14583816 | D4 | direct (N × H) |
| 100. D4×C173 | Q16 | semidirect |
| 113. C22×C173 | C2×Q16 | semidirect |
| 120. C4×C173 | C2×Q16 | semidirect |
| 130. C173 | D4×Q16 | semidirect |
| 224. D4 | #14583816 | direct (N × H) |
| 244. C22 | C2×#14583816 | semidirect |
| 254. C4 | C2×#14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583816 | 2 |
| D4×Dic346 | 2 |
| #26011870 | 2 |
| #26011730 | 2 |
| #26011701 | 2 |
| #26011698 | 2 |
| #26011647 | 2 |
| #26011646 | 2 |
| C4×#14583816 | 2 |
| D4×#13063436 | 2 |
| D4×Q8×C173 | 2 |
| D4×Q16 | 173 |