Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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. C16×D172 | C2 | semidirect |
| 2. #19133947 | C2 | semidirect |
| 3. #19132667 | C2 | semidirect |
| 4. #19132641 | C2 | semidirect |
| 5. C43×#2246 | C2 | semidirect |
| 53. C16×C43 | D8 | semidirect |
| 67. D172 | D16 | semidirect |
| 89. #2246 | D43 | semidirect |
| 110. C43 | #12430 | semidirect |
| 148. C16 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D172 | 2 |
| #19133947 | 2 |
| #19132667 | 2 |
| #19132641 | 2 |
| C43×#2246 | 2 |
| #12430 | 43 |