Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. #19147026 | C2 | semidirect |
| 2. #19136818 | C2 | semidirect |
| 3. #19136632 | C2 | semidirect |
| 4. #19132651 | C2 | semidirect |
| 5. #19132558 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 159. C43 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147026 | 2 |
| #19136818 | 2 |
| #19136632 | 2 |
| #19132651 | 2 |
| #19132558 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C43×#1667 | 2 |
| #12341 | 43 |