Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19149727 | C2 | semidirect |
| 2. #19149726 | C2 | semidirect |
| 3. #19149712 | C2 | semidirect |
| 4. #19149711 | C2 | semidirect |
| 5. #19149708 | C2 | semidirect |
| 6. #19149700 | C2 | semidirect |
| 7. #19149699 | C2 | semidirect |
| 8. C2×#14583816 | C2 | semidirect |
| 9. Q16×D173 | C2 | semidirect |
| 10. #19149687 | C2 | semidirect |
| 11. #137×C173 | C2 | semidirect |
| 87. C173 | #578 | semidirect |
| 94. #137 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149727 | 2 |
| #19149726 | 2 |
| #19149712 | 2 |
| #19149711 | 2 |
| #19149708 | 2 |
| #19149700 | 2 |
| #19149699 | 2 |
| C2×#14583816 | 2 |
| Q16×D173 | 2 |
| #19149687 | 2 |
| #137×C173 | 2 |
| #578 | 173 |