Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19149677 | C2 | semidirect |
| 2. #19149669 | C2 | semidirect |
| 3. #19149669 | C2 | semidirect |
| 4. #19149657 | C2 | semidirect |
| 5. #19149657 | C2 | semidirect |
| 6. #19149656 | C2 | semidirect |
| 7. #19149656 | C2 | semidirect |
| 8. #19149655 | C2 | semidirect |
| 9. #19149644 | C2 | semidirect |
| 13. C2×#14583805 | C2 | semidirect |
| 14. C4⋊C4×D173 | C2 | semidirect |
| 15. C22⋊Q8×C173 | C2 | semidirect |
| 54. C22⋊D173 | Q8 | semidirect |
| 101. C173 | #554 | semidirect |
| 111. C22⋊Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149677 | 2 |
| #19149669 | 2 |
| #19149657 | 2 |
| #19149656 | 2 |
| #19149655 | 2 |
| #19149644 | 2 |
| C4×C22⋊D173 | 2 |
| #19149639 | 2 |
| C2×#14583805 | 2 |
| C4⋊C4×D173 | 2 |
| C22⋊Q8×C173 | 2 |
| #554 | 173 |