Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 2. C2×Q8×Dic173 | C2 | semidirect |
| 3. #26011393 | C2 | semidirect |
| 4. #26011392 | C2 | semidirect |
| 5. #26011348 | C2 | semidirect |
| 6. C4×#14583803 | C2 | semidirect |
| 7. C2×C4×Q8×C173 | C2 | semidirect |
| 10. C2×#14583827 | C4 | semidirect |
| 65. C2×Dic173 | #41 | semidirect |
| 68. Q8×C173 | C22⋊C4 | semidirect |
| 77. C2×C4×C173 | #41 | semidirect |
| 106. C173 | #2341 | semidirect |
| 110. C2×C4×Q8 | D173 | semidirect |
| 164. Q8 | #14583803 | semidirect |
| 184. C2×C4 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583827 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011393 | 2 |
| #26011392 | 2 |
| #26011348 | 2 |
| C4×#14583803 | 2 |
| C2×C4×Q8×C173 | 2 |
| #2341 | 173 |