Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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 | #379×C173 | C2 |
| prime radical | C25×C173 | C22 |
| hypercenter | #379 | D173 |
| hypocenter | C173 | #2848 |
| LCS | G ▷ C23×C173 ▷ C173 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19149656 | C2 | semidirect |
| 3. #26011366 | C2 | semidirect |
| 4. #26011363 | C2 | semidirect |
| 5. #26011349 | C2 | semidirect |
| 8. C22×Dic346 | C22 | semidirect |
| 13. C2×C4⋊Dic173 | C22 | semidirect |
| 14. C2×#14583805 | C22 | semidirect |
| 15. C2×#14583805 | C22 | semidirect |
| 18. #19149586 | C22 | semidirect |
| 39. C24×C173 | Q8 | semidirect |
| 71. C22×C173 | C22⋊Q8 | semidirect |
| 85. C173 | #2848 | semidirect |
| 110. C24 | Dic346 | semidirect |
| 157. C22 | #19149656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic173 | 2 |
| C2×#19149656 | 2 |
| #26011366 | 2 |
| #26011363 | 2 |
| #26011349 | 2 |
| #26011347 | 2 |
| #379×C173 | 2 |
| #2848 | 173 |