Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19136381 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. C2×#14582682 | C2 | semidirect |
| 5. #19134660 | C2 | semidirect |
| 6. #19132691 | C2 | semidirect |
| 7. C2×C43×#357 | C2 | semidirect |
| 43. #13063265 | D4 | semidirect |
| 180. C2×#357 | D43 | semidirect |
| 210. C43 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144239 | 2 |
| #19136381 | 2 |
| C2×#14582712 | 2 |
| C2×#14582682 | 2 |
| #19134660 | 2 |
| #19132691 | 2 |
| C2×C43×#357 | 2 |
| #13387 | 43 |