Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1224 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 | C2×#120×C173 | C2 |
| hypercenter | C2×#120 | D173 |
| hypocenter | C173 | #2847 |
| 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×#19149651 | C2 | semidirect |
| 3. C2×#19149648 | C2 | semidirect |
| 4. #26011371 | C2 | semidirect |
| 5. #26011368 | C2 | semidirect |
| 6. #26011349 | C2 | semidirect |
| 7. C2×#120×C173 | C2 | semidirect |
| 9. C22×C22⋊D173 | C22 | semidirect |
| 15. C2×#14583805 | C22 | semidirect |
| 17. C2×C22⋊Dic173 | C22 | semidirect |
| 18. C2×#14583803 | C22 | semidirect |
| 19. #19149586 | C22 | semidirect |
| 33. C22×Dic173 | D4 | semidirect |
| 43. C24×C173 | D4 | semidirect |
| 88. C22×C173 | #121 | semidirect |
| 98. Dic173 | #120 | semidirect |
| 105. C173 | #2847 | semidirect |
| 110. C2×#120 | D173 | semidirect |
| 133. C24 | C22⋊D173 | semidirect |
| 197. C22 | #19149651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic173 | 2 |
| C2×#19149651 | 2 |
| C2×#19149648 | 2 |
| #26011371 | 2 |
| #26011368 | 2 |
| #26011349 | 2 |
| C2×#120×C173 | 2 |
| #2847 | 173 |