Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#14582713 | C2 | semidirect |
| 3. C2×#14582699 | C2 | semidirect |
| 4. C2×#14582684 | C2 | semidirect |
| 5. #19134660 | C2 | semidirect |
| 6. #19132690 | C2 | semidirect |
| 7. C43×#2159 | C2 | semidirect |
| 61. M32×C43 | D4 | semidirect |
| 178. #2159 | D43 | semidirect |
| 210. C43 | #13387 | semidirect |
| 236. M32 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144244 | 2 |
| C2×#14582713 | 2 |
| C2×#14582699 | 2 |
| C2×#14582684 | 2 |
| #19134660 | 2 |
| #19132690 | 2 |
| C43×#2159 | 2 |
| #13387 | 43 |