Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #124×C173 | C2 |
| hypercenter | #124 | D173 |
| hypocenter | C173 | #535 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14583827 | C2 | semidirect |
| 2. C2×D4×D173 | C2 | semidirect |
| 3. #19149676 | C2 | semidirect |
| 4. #19149675 | C2 | semidirect |
| 5. #19149668 | C2 | semidirect |
| 6. #19149652 | C2 | semidirect |
| 7. #19149649 | C2 | semidirect |
| 8. #19149636 | C2 | semidirect |
| 9. #124×C173 | C2 | semidirect |
| 14. C2×D692 | C22 | semidirect |
| 15. C2×D692 | C22 | semidirect |
| 17. C2×C22⋊D173 | C22 | semidirect |
| 20. C2×C4×D173 | C22 | semidirect |
| 21. #14583805 | C22 | semidirect |
| 23. #14583803 | C22 | semidirect |
| 24. C4×Dic173 | C22 | semidirect |
| 25. C2×Q8×C173 | C22 | semidirect |
| 27. C22⋊C4×C173 | C22 | semidirect |
| 28. C42×C173 | C22 | semidirect |
| 43. C4×D173 | D4 | semidirect |
| 71. C173 | #535 | semidirect |
| 78. #124 | D173 | semidirect |
| 84. C2×Q8 | C2×D173 | semidirect |
| 98. C22⋊C4 | C2×D173 | semidirect |
| 100. C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583827 | 2 |
| C2×D4×D173 | 2 |
| #19149676 | 2 |
| #19149675 | 2 |
| #19149668 | 2 |
| #19149652 | 2 |
| #19149649 | 2 |
| #19149636 | 2 |
| #124×C173 | 2 |
| #535 | 173 |