Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #19146942 | C2 | semidirect |
| 2. #19136820 | C2 | semidirect |
| 3. #19136631 | C2 | semidirect |
| 4. #19133951 | C2 | semidirect |
| 5. #19132555 | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×#1364 | C2 | semidirect |
| 108. D172 | D16 | semidirect |
| 142. #1364 | D43 | semidirect |
| 168. C43 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146942 | 2 |
| #19136820 | 2 |
| #19136631 | 2 |
| #19133951 | 2 |
| #19132555 | 2 |
| #19132549 | 2 |
| C43×#1364 | 2 |
| #12340 | 43 |