Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #19145170 | C2 | semidirect |
| 2. #19145023 | C2 | semidirect |
| 3. #19134267 | C2 | semidirect |
| 4. #19134264 | C2 | semidirect |
| 5. #19134262 | C2 | semidirect |
| 6. #19134259 | C2 | semidirect |
| 7. C2×#14582620 | C2 | semidirect |
| 8. C43×#3147 | C2 | semidirect |
| 80. C2×C8×C43 | D8 | semidirect |
| 136. #3147 | D43 | semidirect |
| 169. C43 | #19616 | semidirect |
| 225. C2×C8 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145170 | 2 |
| #19145023 | 2 |
| #19134267 | 2 |
| #19134264 | 2 |
| #19134262 | 2 |
| #19134259 | 2 |
| C2×#14582620 | 2 |
| C43×#3147 | 2 |
| #19616 | 43 |