Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19137754 | C2 | semidirect |
| 3. #19135432 | C2 | semidirect |
| 4. #19133112 | C2 | semidirect |
| 5. #19132500 | C2 | semidirect |
| 6. #19132447 | C2 | semidirect |
| 7. C43×#1510 | C2 | semidirect |
| 9. #14583217 | C4 | semidirect |
| 12. #14583033 | C4 | semidirect |
| 58. C22⋊(C43⋊C8) | C2×C4 | semidirect |
| 64. C22×D4×C43 | C2×C4 | semidirect |
| 71. C2×C4⋊C4×C43 | C2×C4 | semidirect |
| 243. #1510 | D43 | semidirect |
| 279. C43 | #9343 | semidirect |
| 283. C22×D4 | C4×D43 | semidirect |
| 300. C2×C4⋊C4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145392 | 2 |
| #19137754 | 2 |
| #19135432 | 2 |
| #19133112 | 2 |
| #19132500 | 2 |
| #19132447 | 2 |
| C43×#1510 | 2 |
| #9343 | 43 |