Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 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. #19136204 | C2 | semidirect |
| 3. #340×D43 | C2 | semidirect |
| 4. #19132607 | C2 | semidirect |
| 5. #19132605 | C2 | semidirect |
| 6. #19132603 | C2 | semidirect |
| 7. C43×#1348 | C2 | semidirect |
| 8. C2×#13063348 | C4 | semidirect |
| 13. #14583137 | C4 | semidirect |
| 14. #14583136 | C4 | semidirect |
| 18. #14582936 | C4 | semidirect |
| 32. C2×D344 | C2×C4 | semidirect |
| 53. #13063259 | C2×C4 | semidirect |
| 58. C2×Q16×C43 | C2×C4 | semidirect |
| 63. #107×C43 | C2×C4 | semidirect |
| 192. #1348 | D43 | semidirect |
| 222. C43 | #11704 | semidirect |
| 227. C2×Q16 | C4×D43 | semidirect |
| 255. #107 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144178 | 2 |
| #19136204 | 2 |
| #340×D43 | 2 |
| #19132607 | 2 |
| #19132605 | 2 |
| #19132603 | 2 |
| C43×#1348 | 2 |
| #11704 | 43 |