Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14582721 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. C2×#14582708 | C2 | semidirect |
| 5. C2×#14582677 | C2 | semidirect |
| 6. #19135488 | C2 | semidirect |
| 7. C43×#1972 | C2 | semidirect |
| 11. C2×#13063269 | C4 | semidirect |
| 12. C2×#13063266 | C4 | semidirect |
| 111. C43⋊C16 | C22⋊C4 | semidirect |
| 173. #1972 | D43 | semidirect |
| 199. C43 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583335 | 2 |
| C2×#14582721 | 2 |
| C2×#14582712 | 2 |
| C2×#14582708 | 2 |
| C2×#14582677 | 2 |
| #19135488 | 2 |
| C43×#1972 | 2 |
| #13249 | 43 |