Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D173 |
| commutator, socle, cosocle | C23×C173 | C24 |
| Fitting, prime radical | C2×#120×C173 | C2 |
| hypercenter | C2×#120 | D173 |
| hypocenter | C173 | #2849 |
| LCS | G ▷ C23×C173 ▷ C173 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic173 | C2 | semidirect |
| 2. C2×#19149660 | C2 | semidirect |
| 3. #26011371 | C2 | semidirect |
| 4. #26011363 | C2 | semidirect |
| 5. #26011352 | C2 | semidirect |
| 6. #26011347 | C2 | semidirect |
| 13. C2×#14583805 | C22 | semidirect |
| 16. C2×C22⋊Dic173 | C22 | semidirect |
| 17. #19149586 | C22 | semidirect |
| 29. C22×Dic173 | D4 | semidirect |
| 87. C22×C173 | #123 | semidirect |
| 101. C173 | #2849 | semidirect |
| 189. C22 | #19149660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic173 | 2 |
| C2×#19149660 | 2 |
| #26011371 | 2 |
| #26011363 | 2 |
| #26011352 | 2 |
| #26011347 | 2 |
| C2×#120×C173 | 2 |
| #2849 | 173 |