Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #19142993 | C2 | semidirect |
| 5. #19133279 | C2 | semidirect |
| 6. #19133275 | C2 | semidirect |
| 7. C43×#1276 | C2 | semidirect |
| 96. C42×C43 | SD16 | semidirect |
| 176. #1276 | D43 | semidirect |
| 203. C43 | #10283 | semidirect |
| 287. C42 | #10621873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145725 | 2 |
| #19145522 | 2 |
| #19142993 | 2 |
| #19135423 | 2 |
| #19133279 | 2 |
| #19133275 | 2 |
| C43×#1276 | 2 |
| #10283 | 43 |