Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19136820 | C2 | semidirect |
| 2. #19136819 | C2 | semidirect |
| 3. #19136818 | C2 | semidirect |
| 4. #19134212 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 7. C43×#2240 | C2 | semidirect |
| 108. #2240 | D43 | semidirect |
| 132. C43 | #12509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136820 | 2 |
| #19136819 | 2 |
| #19136818 | 2 |
| #19134212 | 2 |
| #19134209 | 2 |
| C16×C43⋊C8 | 2 |
| C43×#2240 | 2 |
| #12509 | 43 |