Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 105 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. #19136369 | C2 | semidirect |
| 5. #19132696 | C2 | semidirect |
| 6. #19132677 | C2 | semidirect |
| 7. C43×#1945 | C2 | semidirect |
| 20. #14582708 | C4 | semidirect |
| 43. #13063265 | C2×C4 | semidirect |
| 58. #106×C43 | C2×C4 | semidirect |
| 154. #1945 | D43 | semidirect |
| 180. C43 | #12951 | semidirect |
| 211. #106 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063347 | 2 |
| #19136369 | 2 |
| #19136342 | 2 |
| #19136330 | 2 |
| #19132696 | 2 |
| #19132677 | 2 |
| C43×#1945 | 2 |
| #12951 | 43 |