Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D173 | C2 | semidirect |
| 3. #19149677 | C2 | semidirect |
| 4. #19149668 | C2 | semidirect |
| 5. #19149667 | C2 | semidirect |
| 6. #19149664 | C2 | semidirect |
| 7. #19149657 | C2 | semidirect |
| 8. #19149636 | C2 | semidirect |
| 9. C4⋊Q8×C173 | C2 | semidirect |
| 63. C173 | #536 | semidirect |
| 68. C4⋊Q8 | 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×Q8×D173 | 2 |
| #19149677 | 2 |
| #19149668 | 2 |
| #19149667 | 2 |
| #19149664 | 2 |
| #19149657 | 2 |
| #19149636 | 2 |
| C4⋊Q8×C173 | 2 |
| #536 | 173 |