Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D173⋊M16 | C2 | semidirect |
| 2. #19149758 | C2 | semidirect |
| 3. #19149743 | C2 | semidirect |
| 5. #14583836 | C22 | semidirect |
| 10. C4×#10621924 | C22 | semidirect |
| 13. #14583825 | C4 | semidirect |
| 15. C2×Dic346 | C4 | semidirect |
| 19. C2×D4×C173 | C4 | semidirect |
| 56. C173 | #421 | semidirect |
| 68. C2×D4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M16 | 2 |
| #19149758 | 2 |
| #19149743 | 2 |
| C2×#14583825 | 2 |
| #421 | 173 |