Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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. #19145536 | C2 | semidirect |
| 2. #19144392 | C2 | semidirect |
| 3. #19133263 | C2 | semidirect |
| 4. #19133093 | C2 | semidirect |
| 5. #19132986 | C2 | semidirect |
| 6. #19132498 | C2 | semidirect |
| 33. #13063325 | D4 | semidirect |
| 34. #13063325 | D4 | semidirect |
| 45. C4⋊(C43⋊C8) | D4 | semidirect |
| 46. C4⋊(C43⋊C8) | D4 | semidirect |
| 100. C2×D4×C43 | SD16 | semidirect |
| 252. C43 | #10246 | semidirect |
| 324. C2×D4 | #10621883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145536 | 2 |
| #19144392 | 2 |
| #19133263 | 2 |
| #19133093 | 2 |
| #19132986 | 2 |
| #19132498 | 2 |
| C43×#2541 | 2 |
| #10246 | 43 |