Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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. #19147227 | C2 | semidirect |
| 2. #19146260 | C2 | semidirect |
| 3. #19134057 | C2 | semidirect |
| 4. #19134036 | C2 | semidirect |
| 5. #19133841 | C2 | semidirect |
| 6. #19133657 | C2 | semidirect |
| 7. #19133481 | C2 | semidirect |
| 8. C8×Dic172 | C2 | semidirect |
| 9. C43×#1706 | C2 | semidirect |
| 123. Dic172 | D8 | semidirect |
| 179. #1706 | D43 | semidirect |
| 220. C43 | #19888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147227 | 2 |
| #19146260 | 2 |
| #19134057 | 2 |
| #19134036 | 2 |
| #19133841 | 2 |
| #19133657 | 2 |
| #19133481 | 2 |
| C8×Dic172 | 2 |
| C43×#1706 | 2 |
| #19888 | 43 |