Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
532 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 135 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. #19147609 | C2 | semidirect |
| 2. #19136853 | C2 | semidirect |
| 3. #19136648 | C2 | semidirect |
| 4. #19136632 | C2 | semidirect |
| 5. C16×Dic86 | C2 | semidirect |
| 6. C4×Dic344 | C2 | semidirect |
| 7. D16×Dic43 | C2 | semidirect |
| 146. C43 | #33963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147609 | 2 |
| #19136853 | 2 |
| #19136648 | 2 |
| #19136632 | 2 |
| C16×Dic86 | 2 |
| C4×Dic344 | 2 |
| D16×Dic43 | 2 |
| C43×#2246 | 2 |
| #33963 | 43 |