Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 384 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. #19136852 | C2 | semidirect |
| 3. #19136642 | C2 | semidirect |
| 4. #19132640 | C2 | semidirect |
| 5. #19132558 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. C43×#1669 | C2 | semidirect |
| 144. #1669 | D43 | semidirect |
| 170. C43 | #12321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146355 | 2 |
| #19136852 | 2 |
| #19136642 | 2 |
| #19132640 | 2 |
| #19132558 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C43×#1669 | 2 |
| #12321 | 43 |