Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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. #19136432 | C2 | semidirect |
| 3. #19136431 | C2 | semidirect |
| 4. #19132670 | C2 | semidirect |
| 5. #19132569 | C2 | semidirect |
| 6. C8×C43⋊C16 | C2 | semidirect |
| 7. C43×#1335 | C2 | semidirect |
| 25. #13063271 | C8 | semidirect |
| 26. #13063269 | C8 | semidirect |
| 27. #13063268 | C8 | semidirect |
| 28. #13063266 | C8 | semidirect |
| 104. #1335 | D43 | semidirect |
| 125. C43 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136474 | 2 |
| #19136432 | 2 |
| #19136431 | 2 |
| #19132670 | 2 |
| #19132569 | 2 |
| C8×C43⋊C16 | 2 |
| C43×#1335 | 2 |
| #12046 | 43 |