Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #19134213 | C2 | semidirect |
| 4. #19132652 | C2 | semidirect |
| 5. C43×#1370 | C2 | semidirect |
| 50. D344 | Q16 | semidirect |
| 86. #1370 | D43 | semidirect |
| 103. C43 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136743 | 2 |
| #19134213 | 2 |
| C8×D344 | 2 |
| #19132652 | 2 |
| C43×#1370 | 2 |
| #12447 | 43 |