Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
422 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 2. C4⋊C16×D43 | C2 | semidirect |
| 3. #346×D43 | C2 | semidirect |
| 4. #19132554 | C2 | semidirect |
| 5. #19132553 | C2 | semidirect |
| 6. #19132552 | C2 | semidirect |
| 7. C43×#1330 | C2 | semidirect |
| 20. C4⋊(C43⋊C16) | C22 | semidirect |
| 22. #14582675 | C22 | semidirect |
| 25. C43×C4⋊C16 | C22 | semidirect |
| 26. C43×#346 | C22 | semidirect |
| 172. #1330 | D43 | direct (N × H) |
| 178. D43 | #1330 | direct (N × H) |
| 194. C4⋊C16 | C2×D43 | semidirect |
| 197. #346 | C2×D43 | semidirect |
| 198. C43 | C2×#1330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D43 | 2 |
| C4⋊C16×D43 | 2 |
| #346×D43 | 2 |
| #19132554 | 2 |
| #19132553 | 2 |
| #19132552 | 2 |
| C43×#1330 | 2 |
| C2×#1330 | 43 |