Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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. #19136214 | C2 | semidirect |
| 3. #19134640 | C2 | semidirect |
| 4. #19132581 | C2 | semidirect |
| 5. #19132580 | C2 | semidirect |
| 6. #19132579 | C2 | semidirect |
| 7. C43×#1339 | C2 | semidirect |
| 8. C2×D8×D43 | C4 | semidirect |
| 12. #14583153 | C4 | semidirect |
| 14. #14583149 | C4 | semidirect |
| 18. #14582934 | C4 | semidirect |
| 21. #14582681 | C22 | semidirect |
| 23. #14582656 | C22 | semidirect |
| 25. C43×#349 | C22 | semidirect |
| 26. C43×H(3,ℤ/4) | C22 | semidirect |
| 190. #1339 | D43 | semidirect |
| 214. #349 | C2×D43 | semidirect |
| 216. H(3,ℤ/4) | C2×D43 | semidirect |
| 217. C43 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144241 | 2 |
| #19136214 | 2 |
| #19134640 | 2 |
| #19132581 | 2 |
| #19132580 | 2 |
| #19132579 | 2 |
| C43×#1339 | 2 |
| #11868 | 43 |