Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19145598 | C2 | semidirect |
| 2. #19144969 | C2 | semidirect |
| 3. #19133309 | C2 | semidirect |
| 4. #19133193 | C2 | semidirect |
| 5. #19133106 | C2 | semidirect |
| 6. #19132488 | C2 | semidirect |
| 34. #13063325 | D4 | semidirect |
| 35. #13063325 | D4 | semidirect |
| 43. C4⋊(C43⋊C8) | D4 | semidirect |
| 52. #13063236 | D4 | semidirect |
| 231. C43 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145598 | 2 |
| #19144969 | 2 |
| #19133309 | 2 |
| #19133193 | 2 |
| #19133106 | 2 |
| #19132488 | 2 |
| C43×#2657 | 2 |
| #10096 | 43 |