Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
950 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19145510 | C2 | semidirect |
| 2. #19142990 | C2 | semidirect |
| 3. #19133264 | C2 | semidirect |
| 4. #19132428 | C2 | semidirect |
| 5. C43×#1962 | C2 | semidirect |
| 31. C4⋊(C43⋊C8) | D4 | semidirect |
| 37. C4⋊Q8×C43 | D4 | semidirect |
| 38. #127×C43 | D4 | semidirect |
| 76. C42×C43 | D8 | semidirect |
| 133. #1962 | D43 | semidirect |
| 154. C43 | #10280 | semidirect |
| 162. C4⋊Q8 | D172 | semidirect |
| 170. #127 | D172 | semidirect |
| 214. C42 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145510 | 2 |
| #19142990 | 2 |
| #19133264 | 2 |
| #19132428 | 2 |
| C43×#1962 | 2 |
| #10280 | 43 |