Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | C22×D4×C173 | C2 |
| hypercenter | C22×D4 | D173 |
| hypocenter | C173 | #535 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14583826 | C2 | semidirect |
| 2. #19149675 | C2 | semidirect |
| 3. #19149666 | C2 | semidirect |
| 4. #19149650 | C2 | semidirect |
| 5. #19149648 | C2 | semidirect |
| 6. #19149638 | C2 | semidirect |
| 7. C22×D4×C173 | C2 | semidirect |
| 9. C2×Dic346 | C22 | semidirect |
| 10. C2×D692 | C22 | semidirect |
| 12. C2×C22⋊D173 | C22 | semidirect |
| 13. C2×C4×D173 | C22 | semidirect |
| 14. C4⋊Dic173 | C22 | semidirect |
| 16. C22⋊Dic173 | C22 | semidirect |
| 17. C4×Dic173 | C22 | semidirect |
| 37. C2×C4×C173 | D4 | semidirect |
| 57. C173 | #535 | semidirect |
| 60. C22×D4 | D173 | semidirect |
| 95. C2×C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583826 | 2 |
| #19149675 | 2 |
| #19149666 | 2 |
| #19149650 | 2 |
| #19149648 | 2 |
| #19149638 | 2 |
| C22×D4×C173 | 2 |
| #535 | 173 |