Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 2. #19136823 | C2 | semidirect |
| 3. #19136733 | C2 | semidirect |
| 4. #19133984 | C2 | semidirect |
| 5. #19132645 | C2 | semidirect |
| 6. #19132557 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 86. D344 | SD16 | semidirect |
| 141. D4⋊C16 | D43 | semidirect |
| 164. C43 | #12371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146317 | 2 |
| #19136823 | 2 |
| #19136733 | 2 |
| #19133984 | 2 |
| #19132645 | 2 |
| #19132557 | 2 |
| C43×D4⋊C16 | 2 |
| #12371 | 43 |