Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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. #19136397 | C2 | semidirect |
| 3. #19136392 | C2 | semidirect |
| 4. #19132551 | C2 | semidirect |
| 5. D4⋊(C43⋊C16) | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 18. C4⋊(C43⋊C16) | C22 | semidirect |
| 23. C4×C43⋊C16 | C22 | semidirect |
| 25. C43×C4⋊C16 | C22 | semidirect |
| 26. C4×C16×C43 | C22 | semidirect |
| 175. D4⋊C16 | D43 | semidirect |
| 195. C4⋊C16 | C2×D43 | semidirect |
| 200. C4×C16 | C2×D43 | semidirect |
| 201. C43 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×D43 | 2 |
| #19136397 | 2 |
| #19136392 | 2 |
| #19132551 | 2 |
| D4⋊(C43⋊C16) | 2 |
| #19132549 | 2 |
| C43×D4⋊C16 | 2 |
| #11631 | 43 |